March 20, 2013


September 24, 2013, Rhodes Palace Hotel, Rhodes, Greece
Session at the ICNAAM 2013

Christian Corda,
(Italy) Email:;
Thomas Vougiouklis, (Greece) Email and
Richard Anderson,U. S. A., Email

A limitation of 20th century applied mathematics as well as of the covering isomathematics studied in the preceding workshop is that they can only represent reversible systems, namely, systems whose time reversal image verifies causality, conservation and other laws. This is the case for spaceships in a stable orbit in vacuum, atomic structures, particles in accelerators, crystals and many other systems.

The limitation is clearly established by the fact that there is no "time arrow" or equivalent feature in any of of axioms of 20th century applied mathematics, such as those for fields, functional analysis, differential calculus, metric spaces, algebras, geometries, etc. thus automatically implying the jointly treatment of systems moving forward and back ward in time, as typically the case for the Euclidean, Minkowskian, Riemannian and other geometries (evidently due to their "quadratic" line elements).

However, nature is generally characterized by irreversible systems, namely, systems whose time reversal invariance violates causality, energy conservation and other physical laws, as it is the case spaceships during re-entry in our atmosphere, high energy particle collisions, chemical reactions, thermodynamical laws, and many more systems.

Due to their elaboration via 20th century applied mathematics, all mainstream theories developed in the 20th century, such as Einstein's special relativity, quantum mechanics and quantum chemistry, were conceived, developed and rigorously proved solely for the representation of reversible systems.

In view of this limitation well known to "experts" to qualify as such, the political posture of 20th century science was that the irreversibility of nature is "illusory" (sic!) in the sense that, when a macroscopic irreversible system (such as a spaceship during re-entry) is reduced to its elementary constituents (electrons and nuclear constituents), irreversibility "disappears" (sic!) and one recovers the usual reversibility of quantum mechanical particles.

This political posture was disproved by the Italian-American scientist Ruggero Maria Santilli (see his curriculum) during his Ph. D. studies at the University of Torino, Italy, in the mid l960s with the prove of the following:

NO REDUCTION THEOREM: A macroscopic irreversible system cannot be consistently reduced to a finite number of elementary constituents all in reversible conditions and, vice versa, a finite number of elementary particles all in reversible conditions cannot consistently characterize a macroscopic irreversible system.

In this way, Santilli proved that the irreversibility of nature (such as that of a spaceship during re-entry), rather than "disappearing" for the evident political aim of maintaining pre-existing theories, in reality originates at the most elementary level of nature, that of of the constituents of matter. In particular, the interactions experienced by elementary constituents in their origination of irreversibility (such as the interactions between peripheral atomic orbitals of a spaceship and those of our atmosphere) resulted in having the most general possible non-linear, non-local and non-Hamiltonian type, thus being dramatically beyond any dream of even approximate treatment via 20th century mathematics. This established the need for the conduction of systematic mathematical, theoretical and experimental research on irreversibility to which Santilli dedicated his research life.

The studies were also initiated in the 1960s by identifying the origin of the reversibility of 20th century theories, mathematically in the lack of a "time arrow" in the mathematical axioms, and physically in the invariance under anti-Hermiticity of the Lie product,, e.g., between Hermitean operators [A, B] = AB - BA = - [A, B]. where AB is the conventional associative product. In fact, the reversibility of quantum mechanics and chemistry can be reduced to the primitive invariance under anti-Hermiticity of Heisenberg time evolution for a Hermitean operator A,

(1) idA/dt - [A, H ] = -(idA/dt) + [A, H] = 0,

where H is the known Hamiltonian.

Therefore, Santilli initiated his representation of irreversible systems via a generalization of the Lie product [A, B] into a bilinear form (A, B) verifying indeed the axioms to characterize an algebra, but which is neither totally antisymmetric, (A, B) ≠ - (B, A), nor totally symmetric, (A, B) ≠ (B, A), with initial parametric generalization of Heisenberg equation of the following infinitesimal and finite types (see Ref. [1] of 1967 and additional 1960's works quoted in Santilli's CV)

(2) idA/dt = (A, H) = p AH - q HA = m [A, H] + n {A, H}, p = m + n, q = n - m

(3) A(t) = U(t) A(0) W(t) = [exp(i H q t)] A(0) [exp(- i t p H)].

with corresponding classical counterparts here ignored for brevity.

In Ref. [1], Santilli called the new product (A, B) a mutation of the Lie product for certain algebraic reasons but, although the product (A, B) is today known as "deformation of the Lie product." said product (A, B) has great mathematical interest because, according to the American mathematician of the 1940's A. A. Albert, the product (A, B) = pAB - qBA is jointly Lie-admissible and Jordan-admissible since its attached totally antisymmetric product [A, B]* = (A, B) - (A, B) and totally symmetric product {A, B}* = (A, B) + (B, A) verifies all Lie and Jordan axioms, respectively.

It is unfortunate for science that the fundamental Lie- and Jordan-admissibility of Santilli's product (A, B) = pAB - qBA, fully identified in the 1967 paper [1] and numerous subsequent works, were ignored in the virtually complete, rather vast literature in deformations of Lie-algebras from the 1980s on on the particular case (A, B) = AB - qBA in disrespect of Albert's and Jordan's memory, let alone the evident loss of a basic mathematical meaning.

On physical grounds, Santilli's interest was the representation of the time rate of variation of physical quantities, e.g., idH/dt = (H, H) = f(t) ≠ 0, as a covering of conservation laws characterized by Heisenberg equation, idH/dt = [H, H] = 0. this assured that the treatment of irreversible processes based on a well defined covering Lie- and Jordan-admissible algebra, in the same way according to which reversible processes are based on Lie algebras.

When Santilli joined the Department of Mathematics of Harvard University under DOE support in late 1977, he identified the most general known product which is jointly Lie-admissible and Jordan-admissible, and formulated the corresponding operator generalizations of Eqs. (2), (3), today known as Santilli universal Lie- and Jordan-admissible equations (see the original papers [2,3] and monographs [4] written by Santilli at Harvard University),

(5) idA/dt = (A, B)* = ARB - BSA = (ATB - BTA) + (AJB + BJA) = [A, B]* + {A, B}*,

(6) A(t) = U(t) A(0) W(t) = [exp(i H S t)] A(0) [exp(- i t R H)]

with corresponding forward and backward generalizations of Schroedinger equations

(7) H(r, p) S |ψ > = E |ψ>, <&psi | R H = <ψ | E',

where R, S, T, J, R ± N are operators or matrices restricted to be non singular, but otherwise possess an unrestricted, non-linear non-local and non-Hamiltonian dependence on all needed variables, including time t, coordinates r, velocities v, accelerations a, energy e, wavefunctions ψ, their derivatives ∂ψ, etc.
It should be noted that Eqs. (5), (6) maintain the original Lie-admissible and Jordan-admissible character of Eqs. (2),. (3), although in the generalized isotopic sense of the preceding workshop.

By recalling that time evolution (3) is non-unitary by conception (as necessary to exit from the class of unitary equivalence of quantum mechanics), Santilli achieved Eqs. (5), (6)via the application to Eqs. (2), (3) of two most general possible non-unitary transformations according to the rules [2,3]

(8) (A, B) = pAB - qBA → (A, B)* = U (A, B) W = A'RB' - B'SA',

(9) U U ≠ I, WW ≠ I, UW ≠I, A' = UAW, B' = UBW, R = p (UW)-1, S = q (WU)-1.

Santilli finally proved the universality of his product (A, B)* = ARB - BSA by showing that the additional application of to product (A, B)* of two most general possible non-unitary transformations does indeed preserve its Lie- and Jordan-admissible character,

(10) (A, B)* = ARB - BSA → U(A, B)*W = A'R'B' - B'S'A;.

In fact, the algebra with product (A, B)* is the most general known algebra since it includes as particular case all known algebras (defined on a field of characteristic zero), such as associative, Lie, Jordan, Lie-isotopic, Jordan-isotopic,supersymmetric, alternative, flexible, nilpotent and any other possible algebra, thus explaining the denomination of "universality" to Santilli's lie- and Jordan-=admissible equations (5), (6).

Santilli has stated several times in his writings that quantum mechanics has a majestic mathematical and physical structure originating from the unitary character of the time evolution, UU = I. In fact, on mathematical grounds, the unitary structure permits the preservation over time of the basic unit of the base field, 1 → 1' = U1U = 1, with consequential preservation over time of the base field and of the entire mathematics built on it, such as functional analysis, metric spaces, algebras, etc. On physical grounds, the unitary structure permits quantum mechanical laws to remain valid over time, including the prediction of the same numerical values under the same conditions at different times.

Soon after the publication of papers [2,3] of 1978, Santilli discovered that the representation of irreversibility via Eqs. (5), (6), formulated via the mathematics of reversible quantum mechanics is afflicted by mathematical and physical problems that he called "catastrophic" due to the nonunitary character of time evolution (6), UW ≠ I. In fact, on mathematical grounds, such a structure cases the loss over time of the basic unit of the base field, 1 → 1' = U1W ≠ 1, with consequential collapse of the entire mathematical structure of the theory, including the loss of functional analysis, metric spaces, algebras, etc., since all these mathematical formulations are all formulated on the base field.

To understand the physical inconsistencies, one must know that in Santilli's universal Lie-admissible theory, conventional potential interactions are represented via the Hamiltonian H, while all non-linear, non-local and non-potential interactions are represented buy the R and S operators, particularly in view of their unrestricted functional dependence, R = R(t, r, v, a, e, ψ, ∂ψ, ...), S = S(t, r, v, a, e, ψ, ∂ψ, ...). Consequently, any lack of invariance of the R and S operator causes the loss of the originally represented system in favor of a different systems (such as passing from the representation of a member of a nuclear reaction to a proton in the core of the Sun). The catastrophic implication of the lack of invariance here considered is then illustrated by Eq. (10) where one can see the change of the value of the R and S operators under a non-unitary transform.

The above aspects were formalized by Santilli and others via the following:

THEOREM OF CATASTROPHIC INCONSISTENCIES OF NON-CANONICAL AND NON-UNITARY THEORIES (see Ref. [5] and preceding literature quoted therein): When formulated via the mathematics of quantum mechanics (numerical fields, functional analysis, differential calculus, etc.) non-unitary time evolutions are afflicted by the following inconsistencies: 1) Lack of preservation over time of the numerical value of the units used for measurements; 2) Lack of prediction of the same numerical values under the same conditions at different times; 3) Lack of preservation over time of Hermiticity, with consequential loss of observability (Lopez's Lemma); and other inconsistencies. Corresponding inconsistencies exist for non-canonical time evolution when elaborated via the mathematics of classical Hamiltonian mechanics.

The above theorem establishes the catastrophic inconsistencies of numerous 20th century theories, including [5]; dissipative nuclear processes; q- and k-deformations; quantum groups; Weinberg's non-linear theory; squeezed state theories; non-unitary statistical theories; super symmetric theories; Kac-Moody theories; and any other theory with a non-unitary time evolution as elaborated in the 20th century, namely, via the mathematics of unitary theories.

Despite the wide propagation of the above inconsistency theorem and its publication in various additional refereed journal, it is unfortunate for science that both authors and editors alike have continued to publish non-unitary theories without the dismissal, or at least the quotation of the literature in their catastrophic inconsistencies.


The picture in the left illustrates the reversibility over time, with consequential applicability of Einsteinian theories, during the acceleration of protons at the CERN large collider. The picture in the right illustrates the clear irreversibility over time of the subsequent scattering of protons on a target under which Einsteinian and relativistic scattering theories have been established as being inapplicable on mathematical, theoretical and experimental grounds. Note the inconsistency of the reduction at CERN of the scattering region to isolated points, as a tacit but evident attempt at maintaining Einsteinian theories throughout the scattering process, which inconsistency is established by the above quoted No reduction Theorem.

Immediately following the publication by Santilli in 1978 of his universal Lie-admissible algebra for the representation of irreversible processes, while admitting reversible Lie and Lie-isotopic formulations as particular case, S. Adler of the Institute for Advances Studies in Princeton published paper [11] showing that Santilli's Lie-admissible algebras constitute a clear covering of unsymmetrical theories due to their inclusion of commutators and anti commutators, as per Eqs,. (5). Unfortunately, Adler received the mandate from his bothers at Harvard University to stop working in the field, and no additional contact of scientific action was possible from Adler.

Similarly, a few years later, J. Ellis of the Theoretical Division at CERN reconsidered Santilli's Lie-admissible theory and published with E. Mavromatos and D. V. Nanopoulos paper [13[ which is one of the most rigorous representations of the irreversibility of interior astrophysical dynamics. Subsequently, Ellis invited Santilli to deliver at CERN a presentation in 1992 of hadronic mechanics and its representation of irreversibility. However, exactly as it had happened to Adler, Ellis too received the mandate, this time by notorious organized interests on Einstein controlling CERN, to halt all research in the field. and again no additional contact or scientific action of any type became possible from Ellis.

The above organized scientific crime on Einstein is still acting in a fully unperturbed fashion to this day via the abuse of academic power for the suppression of undesired research.. It should be indicated that, in the event organized scientific interest on Einstein had not interfered with the research by independent scientists such as Adler, Ellis, and others, their studies on irreversibility would have prevented the waste of trillions of dollars in the search for imaginary particles that cannot be even consistently defined, let alone verified with a minimal of scientific dignity. As Santilli's puts it: "It is sad to see that individuals who have devoted their lives to the pursuit of new scientific knowledge have to serve in such a vile manner the clear scientific crime on Einstein currently controlling scientific knowledge via the abuse of academic authority, the suppression of any shadow of scientific democracy and the elimination of the historical process of debating open fundamental issues, this subservience occurring without a public denunciation, thus implying complicity in true scientific crimes.

The workshop shall dedicate a special session to the inconsistencies of the research at CERN caused by their lack of proper representation of the irreversibility over time of high energy scattering studied in technical details in Refs. [12] and denounced in the Announcement of December 15, 2011

The resolution of the inconsistencies of non-canonical and non-unitary theories required Santilli two decades of intense research, since the needed resolution requires the construction of basically new mathematics, structurally broader than the isomathematics of the preceding workshop. Evidently, we cannot possibly review in these introductory notes the new mathematics, and have to refer the serious scholar to the original literature, particularly memoirs [6.7.8] and monographs [9]. Nevertheless, an identification of at least the most salient points can be useful to the serious scholar interested in the pursuit of new knowledge.

To begin, in the 1980s, Santilli went back to the original observation of the 1960 that the 20th century applied mathematics cannot represent irreversibility because it lacks a "time arrow" in its basic axioms, such as those of number theory, functional analysis, differential calculus, etc. Following trial and errors, he discovered that a given field F(n,•,1) of numbers n (real, complex or quaternionic numbers) with conventional associative product n•m = nm, and unit 1, can be decomposed into two fields F(n,→,1) and F(n,←,1) with ordered multiplications to the right and the left, n→m, and n←m, respectively, and still verify all axioms of a numeric field. This discovery allowed Santilli to introduce the representation of motion forward and backward in time via corresponding ordering in the most fundamental mathematical notion, that of numeric fields.

It was easy to see that, despite its fundamental character for irreversibility, the mathematics constructed lover the ordered fields F(n,→,1) and F(n,←,1) are grossly insufficient to achieve the invariance of the universal Lie- and Jordan-admissible equations (5), (6), as necessary for mathematical and physical consistency.

Following years of to great hesitation due to reverence for Gauss, Caley, Hamilton and other mathematicians, Santilli had no other choice than reinspecting the historic classification of numbers, by discovering its incompleteness because the abstract axioms of a numeric field, not only allow an ordering of the product, but also remain valid under the most general conceivable notion of multiplicative unit and related product.

This lead to Santilli forward and backward genofields that are given by the set F(n,→, I) and F(n,←,I) with:

elements called forward and backward genonumbers

(11) n = n I, n = I n,

forward and backward genounits characterized by invertible, but otherwise arbitary quantities (generally outside the original field F) with an arbitrary functional dependence on all needed variables,

(12) I = I(t, r, v, a, e, ψ, ∂ψ, ...) = 1 / S.

(13) I = I(t, r, v, a, e, ψ, ∂ψ, ...) = 1 / R,

corresponding forward and backward multiplication

(14) n → m = n S m, n ← m = n R m,

and related identities valid for all elements of the respective genofields

(15) I → n = n, I ← n = n.

Santilli then constructed two generalized mathematics over the respective genofields F(n,→, I) and F(n,←,I) today knows as Santilli forward and backward genomathematics, respectively, that include the novel forward and backward functional analysis, differential calculus, metric spaces, algebras, symmetries, etc.

The prefix "geno" was introduced by Santilli in the original papers of 1978 [2,3] following a suggestion by Mrs. Carla Santilli, in the Greek sense of denoting the induction of new axioms, while the prefix "iso" of the preceding workshop was suggested, also by Mrs. Santilli, to denote the preservation of the original axioms.

A technical knowledge of the achievement of invariance of Santilli's Lie- and Jordan-admissible theories via genomathematics is useful to the scholar interested in research resisting the test of time (the mathematically not inclined reader can see an elementary proof in ref. [10]). The representation of irreversibility is not only assured by the selection of the forward genomathematics, but also by its inequivalence with the backward genomathematics.

The non-unitary generalization of quantum mechanics introduced by Santilli in Refs.[2,3] under the name of hadronic mechanics with basic equations (5)-(7) is today also called Santilli genomechanics and referred to the same equations when elaborated via forward genomathematics. Isomathematics studied in the preceding workshop characterizes a particular case of hadronic mechanics known as isomechanics while the broader hypermathematics of the next workshop characterized the broader hypermechanics.

All preceding formulations solely apply for the representation of the irreversibility of matter. Santilli forward and backward isodual genomathematics for antimatter is the image of the preceding genomathematics under the isodual map (anti-Hermiticity) applied to all quantities and operations of genomathematics [9].

In the event seeded in a sound mathematical environment, Santilli Lie-admissible formulations can indeed promote a renaissance in mathematics, since they can stimulate a covering of the virtual totality of the 20th century mathematics. Among a virtually endless number of possible advances in pure mathematics, we quote:

1) The birth of a basically new modular theory since the representation theory of Lie algebras, as well as the treatment of the conventional Schrodinger's equation, can be entirely done via one single conventional, associative module with right actions of the type H |ψ> = E | ψ >, the conjugate left action being not necessary as well known. As illustrated by Eqs. (7), Santilli's Lie-admissible formulations require instead the use of genobimodule [9] in the sense of a bimodule with inequivalent action to the right and to the left,

(16) H → | ψ> = H S | ψ> = E | ψ >, <ψ | ← H = <ψ | R H = <ψ | E.

The non-triviality of the lifting is then illustrated by the inequivalence of the right and left action (i.e., by the basic property E ≠ S) as well as by the different values EE.

2) A consequential genobimodular lifting of the entire 20th century pure and applied mathematics that has solely been touched by Santilli's solitary studies.

3) A structural generalization of all branches of Lie's theory, from its current form solely applicable to linear, local-differential, Hamiltonian, and reversible systems, to a covering theory capable of treating the most general known non-linear, non-local, non-Hamiltonian and irreversible systems, with manifest value for the structural advancement of mathematics.

By noting that, despite their birth in 1967 [1], Lie-admissible formulations of irreversible systems have been studied to date by a physicist in the invariant form needed for physical applications, the need for a collegial participation by the mathematics community appears evident.

The non-initiated mathematician reading these note should know that the virtual entire, rather large literature existing in non-associative algebras in general, and on Lie-admissible algebras in particular, is inapplicable for physical applications because formulated on conventional fields and related mathematics, thus violating the condition of invariance necessary for physical meaning.

As easily predictable, the availability fir the first time in scientific history of a rigorous mathematical representation of irreversibility has permitted numerous basic advances in physics and chemistry, among which we indicate in chronological order of appearance:

Lie-admissible covering of supersymmetries.
Immediately following the appearance of memoirs [2,3] of 1978, Steven Adler of the Institute for Advanced Studies in Princeton, NJ, published paper [11] essentially proposing Santilli's Lie-admissible formulations as a covering of supersymmetries that, since they link bosons and Fermions, require a mixture of antisymmetric and symmetric contributions, e.g., of the type

(17) (Jr, Js) = [Jr, Js] + {Jr, Js}.

Adler pioneering research was halted by his peers in Princeton, Cambridge and elsewhere because "Santilli Lie-admissible theories" are synonym of the undesired structural surpassing of Einstein's theories, since the latter are strictly reversible over time, while the former are irreversible by conception and construction. Adler's halting of research in the field was unfortunate for science because Santilli had already shown in Sect. 5 of Ref. [3] that non-unitary effects due to irreversible processes caused by deep overlapping of wavepackets implies essentially prohibits particle exchanges at very high energies with hyperdense scattering regions, and at best implies a renormalization of all intrinsic characteristics of particles, thus including the mass as studied in details in the recent series of papers [12]. Consequently, Adler's continuation of his research on Santilli's Lie-admissible formulations may have likely prevented the waste of billions of dollars at CERN in the search of the Higgs boson since its very existence is impossible under a quantitative representation of the irreversibility of very high energy scattering process and, in the event that the Higgs boson might exist, there is no known rigorous possibility that the value of its mass is that predicted by reversible scattering theories (see also the figure).

Lie-admissible structure of interior astrophysical problems.
In 1996, John Ellis (then head of the Theoretical Division at CERN) and his associates recognized that interior problems of astrophysical bodies can be best represented via Santilli's Lie-admissible formulations due to their inherent irreversibility which is manifestly beyond the representational capabilities of quantum mechanics. Unfortunately, Ellis too was forced to halt his research on Lie-admissibility for the same reasons and organized interests, this time at CERN, that prevented Adler from continuing his studies in the field. This was also unfortunate for science because, had Ellis been able to continue his studies, there would have been the savings of additional billions of dollars in theoretical studies and the launching of very expensive probes seeking the detection of the hypothetical dark matter, dark energy and all that since their very existence is prohibited under a quantitative representation of the irreversibility of interior astrophysical problems (see also the studies on Santilli IsoRedShift of the preceding workshop).

Geometric representation of interior gravitational problems,
As it is well known by experts but generally not spoken, Einstein's gravitation solely provides a geometric representation of exterior, fully reversible gravitational problems that, as such, has no chance of achieving a representation of interior gravitational problems, e.g., due to incompatibility with thermodynamics, particularly in view of the No reduction Theorem indicated earlier. In paper [14] of 1998, Santilli showed that his genomathematics allows a quantitative representation of interior gravitational problems with the most general possible functional dependence of the metric and its lack of symmetric character as necessary to introduce the "arrow of time" in geometry. The solution is given by the genotopies of the Minkowskian line element

(18) x2 → = {xμ [Sμν gνρ] xρ} I,

where one recognize the multiplication by the genounit (necessary for the line element to be a genonumber); S is now a 4x4 non-singular non-symmetric matrix with unrestricted functional dependence of its elements, S = S(t, r, v, a, e, .....); g = g(r) is the conventional Riemannian metric; and I = 1/S. A surprising aspect is that, when formulated via genomathematics and its genodifferential calculus, the Riemann-Santilli genogeometry is locally isomorphic to the conventional geometry because the mutation of the Riemannian metric g → Sg is compensated by the inverse mutation of the unit of the geometry, I → 1/S (see also Refs. [7]). It should be additionally noted that, as also well known by experts but not generally spoken, Einstein gravitation has no means whatsoever to characterize the gravitational field of a neutral body. This additional problem was solved by Santilli with his isodual theory of antimatter [15] that did indeed achieve the first known consistent representation of the gravity of neutral antimatter, the addition of a charge being trivial.

Nuclear fusions without harmful radiations.
As it is also well known by experts but generally not spoken, the quantum mechanical amplitude for nuclear fusions has no arrow of time. Therefore, quantum mechanics predicts the fusion of two nuclei into a third as well as its time reversal image consisting of the spontaneous decay of the third nucleus into the original two ()xx) N1 + N2 → N3, N3 → N1 + N2

the latter reaction being in violation of causality, conservation and other laws. Santilli developed the irreversible Lie-admissible branch of hadronic mechanics, specifically, to resolve these inconsistencies as a condition to achieve a consistent representation of nuclear fusions. Following decades of silent work, Santilli developed the theory of Intermediate Controlled Nuclear Fusions (ICNF) without the emission of harmful radiations (such as neutrons) and without the release of radioactive waste. In 2011, Santilli released paper [16] on the ICNF of Nitrogen (14) from Deuterium 912) and Carbon (12) in which, as one can see, when Nitrogen is synthesized, there can be no possible release of any neutron or other harmful radiations. When Nitrogen is not synthesized, the power used by the reactor is about one million times short of the energy needed to break down the Deuterium and/or Carbon nuclei as a necessary to produce neutrons. Subsequently, also in 2011, Santilli released paper [17] on the synthesis of the Silica (28) from Oxygen (16) and Carbon (12) also without harmful radiations. ICNF have been first independently verified by Leon Ying and his associates from Princeton, NJ, and ICNF are currently under systematic experimental verifications for possible reporting at this workshop.

First connection between mechanics and thermodynamics.
As it is also well known by experts but generally not spoken, classical Hamiltonian mechanics and quantum mechanics have been developed to represent conservation laws for reversible systems and, as such, they are irreconcilably incompatible with thermodynamics. Anil Bhalekar has initiated pioneering studies in showing that, due to its irreversibility, Santilli Lie-admissible mechanics does indeed allow a direct connection to thermodynamics (see Ref. [19,20] and contributions to be presented at this workshop).

Consistent treatment of irreversible chemical reactions.
As it is also well known by experts but generally not spoken, quantum chemistry is a structurally reversible theory since it is based on quantum mechanical actions. Therefore, quantum chemistry is conceptually, mathematically and chemically incompatible with chemical reactions due to their general irreversible character. In fact, quantum chemistry predicts not only a given chemical reaction such as the synthesis of water, but also the spontaneous decay of the water molecule into the original constituents

(xx) H2 + O2/2 → H2O, H2O → H2 + O2/2,

the latter also violating causality, conservation and other laws. Following the identification of the foundations of the Lie-admissible irreversible branch of hadronic mechanics, Santilli has identified the foundations of the corresponding covering of quantum chemistry under the name of hadronic chemistry, that has already achieved remarkable results while additional basic advances are under way by a number of scholars (see monograph [21], Tandge quite readable review [22], and proceedings [23].

All scientists interested in participating in this workshop must apply to one of the organizers with a statement of interest, whether as a speaker or as auditor, and include a CV. No participant will be admitted to this workshop without the written authorization by one of the organizers.

the R. M. Santilli Foundation has allocated financial support for participation to this workshop, including the support of travel, lodging and registration, which funds are available on a first come first serve basis for all qualified speakers or auditors, including graduate students. The Foundation has additionally allocated $1,000 (one thousand U. S. dollars) for the writing of a review or research papers, provided it is based on Lie-admissible formulations and related genomathematics. For all financial support, following and only following written acceptance by one of the organizers, please contact
Richard Anderson
Trustee, the R. M. Santilli Foundation


[1] R. M. Santilli, Nuovo Cimento {\bf 51}, 570 (1967), available in free download from the link\\

[2] R. M. Santilli, " Hadronic J. 1, 223-423 (1978), available in free pdf download from \\

[3] R. M. Santilli, Hadronic J.1, 574-901 (1978), available in free pdf download from \\

[4] R. M. Santilli, Foundation of Theoretical Mechanics, Volume I (1978) [4a], and Volume II (1982) [4b], Springer-Verlag, Heidelberg, Germany, available as free download from\\

[5] R. M. Santilli, "Origin, problematic aspects and invariant formulation of classical and operator deformations," Intern. J. Modern Phys. {\bf 14}, 3157 (1999, available as free download from

[6] R. M. Santilli, Algebras, Groups and Geometries 10, 273 (1993), download
[7] R. ~M.~Santilli, Rendiconti Circolo Matematico Palermo, Suppl. {\bf 42}, 7-82 (1996), available as free download from\\

[8] R. M. Santilli, ''Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels," Nuovo Cimento B {bf 121}, 443 (2006),

[9] R. M. Santilli, Elements of Hadronic Mechanics, Vol. I and II, Second Edition (1995), Ukrainan Academy of Sciences\\

[10] R. M. Santilli, Found. Phys. {\bf 27}, 1159 (1997), available in free pdf download from the link \\

[11] S. Adler, Phys. Rev. 17, 3212 (1978)

[12] R. M. Santilli and A. O. E. Animalu, "Nonunitary Lie-isotopic and Lie-admissible scattering theories of hadronic mechanics,"Papers I, II, III, IV and V, by , in the Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, C. Corda, Editor, Kathmandu University (2011)

[13] J. Ellis, N. E. Mavromatos and D. V. Nanopoulos in Proceedings of the Erice Summer School, 31st Course: From Superstrings to the Origin of Space-Time, World Scientific (1996).

[14] R. M. Santilli, "Iso-Minkowskian geometry for the gravitational treatment of matter and its isodual for antimatter," Intern. J. Modern Phys. D {\bf 7}, 351 (1998),

[15] R. M. Santilli, Isodual Theory of Antimatter with Application to Antigravity, Grand Unification and the Spacetime Machine, R.M.Santilli, Springer 2001

[16] R. M. santilli, "Experimental Confirmation of Nitrogen Synthesis from deuterium and Carbon without harmful radiations,"New Advances in Physics Vol. 4, page 29, 2011

[17] R. M. Santilli, "Additional Confirmation of the "Intermediate Controlled Nuclear Fusions" without harmful radiation or waste," in the Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, X. Corda, Editor, Kathmandu University (2011) pages 163-177

[18] Robert Brenna, Theodore Kuliczkowski, Leong Ying "Verification of Santilli intermediate Controlled Nuclear Fusions without harmful radiations a and the production of magnecular clusters," New Advances in Physics, Vol. 5, page 9 (2011)

[19] Anil A. Bhalekar, "A Preliminary Attempt on the Reframing of Thermodynamics of Irreversible Processes Using Santilli's Hadronic Mechanics," Hadronic J., 35, 221-236 (2012).

[ [20] Anil A. Bhalekar, "On the Geno-GPITT Framework," AIP Conf. Proc. 1479, 1002-1005 (2012);

[21] R. M. Santilli, Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels, Kluwer Academic Publishers (2001).

[22] V. Tandge, "Advances in hadronic chemistry and its applications," in press

[23] C. Corda, Editor, Proceedings of the 2011 International Conference on Lie-admissible Formulations for Irreversible Processes, Kathmandu University, Nepal