Electronic Journal of Theoretical Physics

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ISSN 1729-5254


Majorana Prize







Majorana Year

Ettore Majorana (1906-1938?)

"There are many categories of scientists, people of second and third rank, who do their best, but do not go very far. There are also people of first-class rank, who make great discoveries, fundamental to the development of science. But then there are the geniuses, like Galileo and Newton. Well Ettore Majorana was one of them. Majorana had what no one else in the world had."

Enrico Fermi to Giuseppe Cocconi.




Electronic Journal of Theoretical Physics aims to promote a style in theoretical physics able to join together the most advanced researches in different areas with a critical approach to very foundational questions.


On the occasion of the Majorana Centenary in 2006 and the editing of the Special Issue about his Legacy in Contemporary Physics, the Electronic Journal of Theoretical Physics has established a prize in memory of the great Sicilian physicist Ettore Majorana (1906 - 1938), universally known for Quantum-Relativistic Equation for any Spin and Neutrino Mass Theory.


The "Majorana Medal" is an annual prize of excellence for the researchers who showed peculiar creativity, critical sense and mathematical rigour in theoretical physics - in its broadest sense.


The Majorana Prize committee announces the names of the laureates in January. The prize is then formally awarded on March 27, the anniversary of Ettore Majorana disappearance.


The prize awarded by the Electronic Journal of Theoretical Physics (EJTP) consists of a medal and an award certificate administrated by the Electronic Journal of Theoretical Physics (EJTP) copyright and intellectual property.


The prize will be awarded to three different categories:

1- The Best Person in Physics.

2- The Best Special Issue Paper.

3- The Best Paper.


The first category is a tribute EJTP pays to an outstanding personality in Physics. The second and third categories are directly related to EJTP editorial activity.


2006 Majorana Prizes Laureates:


EJTP Best Person in Physics 2006


Erasmo Recami (Univ. Bergamo, INFN, Italia):


For his fundamental contributions in: Extended Relativity, in particular on the Theory of Tachyonic Objects and the role of iper-c velocity in Field Theory; Strong Gravity and Semiclassical Models of Particle Structure; Analysis of the Tunneling Processes at Imaginary Time.

For his constant and critical attention towards Physics Foundations and its History, as it is shown by his excellent and fundamental work on Ettore Majorana life and science.


Ennakkal Chandy George Sudarshan ( University of Texas, Austin):


For his fundamental contributions in:

Quantum Field Theory and particle Physics, in particular on Tachyons; Formalism of Dynamic Maps in Open Quantum Systems; Sudarshan-Glauber Representation in Quantum Optics.

For his epistemological work on Indian Phylosophy and Modern Physics connections.


EJTP Best Paper Special Issue 2006, "Majorana Legacy":


Jason Zimba (Bennington College, Vermont, USA):


"Anticoherent " Spin States via the Majorana Representation.

For his elegant geometric representation on  non-local states in Riemann - Majorana Sphere


In this article we define and exhibit '' anticoherent" spin states, which  are in a sense '' the opposite" of the familiar coherent spin states. Since the familiar coherent states are as "classical" as spin states can be, the anticoherent states may turn out to be better candidates for applications involving non-classical behaviors such as quantum entanglement.  Thanks to the Majorana representation of spinors as 2s-tuples of points on the Riemann sphere, classes of anticoherent states are easy to find; the development of such examples also leads us into some curious geometry involving the perfect solids.


EJTP Best Annual Paper:


Gordon W. Semenoff ( Univ. British Columbia, Canada) and Pasquale Sodano(Univ. PG, Italia):


Stretching the Electron as Far as it Will Go.

For their research on Majorana Zero Modes.


Effects associated with the existence of isolated zero modes of Majorana fermions are discussed. It is argued that the quantization of this system necessarily contains highly extended quantum states and that populating and depopulating such states by interacting with the quantum system leads to long-ranged teleportation-like processes. Also leads to spontaneous violation of fermion parity symmetry. A quasi-realistic model consisting of a quantum wire embedded in a p-wave superconductor is discussed as an explicit example of a physical system with an isolated Majorana zero mode.




2007 Majorana Prizes Laureates:


EJTP Best Person in Physics 2007:


Lee Smolin (Perimeter Institute for Theoretical Physics

31 Caroline St. N. Waterloo Ontario, Canada)


For his fundamental contributions to Unified Theories and Quantum Gravity, and - at the same - for his critical attitude in this field. His mathematical mastery and elegance have never turned into a rhetorical artifact so making him able to go to the physical core of the problem and providing the whole community of physicists with an example of style.


EJTP Best Paper Special Issue 2007, " Physics of Emergence and Organization": This book has been Published by the World Scientific.


Eliano Pessa (Centro Interdipartimentale di Scienze Cognitive, Universit`a di Pavia and Dipartimento di Psicologia, Universit`a di Pavia Piazza Botta, 6 , 27100 Pavia, Italy)


"Phase Transitions in Biological Matter" EJTP Volume 4, Special Issue 16 part One.


In this paper we will deal with usefulness of physical theory of phase transition in order to describe phenomena of change occurring in the biological world. In particular, we will assess the role of quantum theory in accounting for the emergence of different forms of coherence seemingly characterizing a number of biological behaviours. In this regard we will introduce some arguments that, while supporting the convenience (as well as the unavoidability) of resorting to a quantum-theoretical framework to describe biological emergence, point to the need for a suitable generalization of actual quantum theory. Some possible ways to achieve such a generalization will be shortly discussed.



EJTP Best Annual Paper:


Marcello Cini (Dipartimento di Fisica, Universita’ La Sapienza, Roma, Italy)


" Mental and Physical Objects in Quantum Mechanics: Any Lessons for other Disciplines?"  EJTP Volume 4, Issue 15 (July 2007);



The standard formulation of Quantum Mechanics has raised from its beginning animated discussions about the interpretation of the counterintuitive properties of mental objects (wave functions or Schrödinger waves) introduced to represent the properties of the physical objects.Two questions have since then been formulated to which a universally accepted answer is still lacking. The first one (Bohr, von Neumann) concerns the ontological nature of physical reality (the existence of classical objects) and the role of the observer (wave packet collapse) in assessing it. The second one is the non local character of quantum physical quantities (Einstein Podolski Rosen [EPR] long distance correlation of particles). An alternative formulation of Quantum Mechanics, originally proposed in 1932 by Eugene Wigner, taken up by Richard Feynman in 1987, and reelaborated by myself in the years from 1998 to 2003, is possible. The mental objects of standard Quantum Mechanics (Schrödinger waves) no longer appear in this new formulation and are replaced by new ones (Wigner functions) which do not show any more the puzzling properties which worried Einstein. My conclusion from the preceding discussion is that different explanations of a given set of experimental data may be derived according to the different nature of the mental objects introduced to represent the properties of the physical objects involved. The confusion between these two kind of objects may be, however, very misleading. I will finally discuss two examples of this conclusion from Biology and Economics.



2008 Majorana Prizes Laureates:


EJTP Best Person in Physics 2008:

Geoffrey F. Chew  (Theoretical Physics Group, Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, U.S.A.)


For his fundamental contributions in thinking the whole Particle Physics following a philosophy which is giving new impulses to the most recent Physics' areas and for his latest contributions on Quantum Cosmology.


EJTP Best Paper Special Issue 2008, " Lev Davidovich Landau and his Impact on Contemporary Theoretical Physics (Horizons in World Physics, Volume 264) ": This book has been Published by the Nova Science Publishers .


Hagen Kleinert (Institut fur Theoretische Physik, Freie Universitat Berlin, Arnmimallee 14, D-14195 Berlin, Germany)


"From Landau's Order Parameter to Modern Disorder Fields ".


Landau's work was crucial for the development of the modern theory of phase transitions. He showed that such transitions can be classified by an order parameter, which in the low-temperature phase becomes nonzero. Together with Ginzburg he made this order parameter a spacetime-dependent order field and introduced a local energy functional whose extrema yield field equations and whose fluctuations determine the universal critical behavior of second-order transitions. In the same spirit, but from a dual point of view, I have developed in the last twenty years a disorder field theory that describes phase transitions via the statistical mechanics of grand-canonical ensembles of vortex lines in superfluids and superconductors, or of defect lines in crystals. The Feynman diagrams of the disorder fields are pictures of the vortex or defect lines. A nonzero ground state expectation value of the disorder field at high temperature signalizes the proliferation of line like excitations in the ordered phase. It was this description of the superconductor that led in 1982 to a first understanding of the order of the superconducting phase transition. Recent experimental progress in the critical regime of high-TC superconductors will be able to verify the predicted tricritical point of the Ginzburg parameter \kappa \approx 0.8/ \sqrt{2}  where the second-order transition becomes first-order.



S. Esposito and G. Salesi ( Dipartimento di Scienze Fisiche, Universit`a di Napoli “Federico II” & I.N.F.N. Sezione di Napoli, Complesso Universitario di M. S. Angelo, Via Cinthia, 80126 Naples, Italy,

Facolt`a di Ingegneria, Universita Statale di Bergamo, viale Marconi 5, 24044 Dalmine (BG), Italy & I.N.F.N. Sezione di Milano, via G. Celoria 16, I-20133 Milan, Italy )


"Generalized Ginzburg-Landau Models for Non-conventional Superconductors"


We review some recent extensions of the Ginzburg-Landau model able to describe several properties of non-conventional superconductors. In the first extension, s-wave superconductors endowed with two different critical temperatures are considered, their main thermodynamical and magnetic properties being calculated and discussed. Instead in the second extension we describe spin-triplet superconductivity (with a single critical temperature), studying in detail the main predicted physical properties. A thorough discussion of the peculiar predictions of our models and their physical consequences is as well performed.



Giuseppe Vitiello (Dipartimento di Matematica e Informatica Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Salerno Universitá di Salerno, 84100 Salerno, Italia)


Quantum Field Theory Project 2008


"Topological Defects, Fractals and The Structure of Quantum Field Theory".


In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical structure of quantum field theory with particular reference to the processes of non-equilibrium symmetry breaking. The functional realization of fractals in terms of the q-deformed algebra of coherent states is also presented. From one side, this sheds some light on the dynamical formation of fractals. From the other side, it also exhibits the fractal nature of coherent states, thus opening new perspectives in the analysis of those phenomena where coherent states play a relevant role. The global nature of fractals appears to emerge from local deformation processes and fractal properties are incorporated in the framework of the theory of entire analytical functions.




EJTP Best Annual Paper:


N. I. Farahat and W. I. Eshraim (Department of Physics, Islamic University of Gaza P.O.Box 108, Gaza, Palestine, Via Israel)


" Hamilton-Jacobi Formulation of A Non-Abelian Yang-Mills Theories"  EJTP Volume 5, Issue 17 (March 2008);



A non-Abelian theory of fermions interacting with gauge bosons is treated as a constrained system using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. The integability conditions are satisfied, and the set of equations of motion is integrable. A comparison with Dirac’s method is done.



2009 Majorana Prizes Laureates:


EJTP Best Person in Physics 2009:

Mario Rasetti (Dipartimento di Fisica, Politecnico di Torino,

Corso Duca degli Abruzzi 24; 10129 Torino (Italy).

Fondazione ISI - Institute for Scientific Interchange,

Viale Settimio Severo, 65; 10133 Torino (Italy)


For his fundamental contributions to Non-linear Physics, Quantum Field Theory and Quantum Information in a rarely elegant and rigorous global vision. And for his promoting the scientific international interdisciplinary collaboration.




EJTP Best Annual Paper:


J. P. Singh (Department of Management Studies, Indian Institute of Technology Roorkee, Roorkee 247667, India)


" Relativistic Spin Operator with Observers in Motion"  EJTP Volume 7, Issue 23 (March 2010); and for his several innovative contributions to different Physics' areas from Quantum Mechanics to Econophysics.



We obtain transformation equations for the Bell basis states under an arbitrary Lorentz boost and compute the expectation values of the relativistic center of mass spin operator under each of these boosted states. We also obtain expectation values for spin projections along the axes.



2010 Majorana Prizes Laureates:


EJTP Best Person in Physics 2010:

N. David Mermin (Laboratory of Atomic & Solid Physics

Cornell University, Ithaca, NY 14853-2501, USA)


For his fundamental contributions on the solid state physics, quantum field theory and statistical mechanics, especially Mermin-Wagner theorem and its remarkable applications. And for his promoting the scientific international interdisciplinary collaborations.



EJTP Best Annual Paper 2010:


Tuluzov, and S. I. Melnyk (Kharkiv Regional Centre for Investment, of.405, vul. Tobolska, Kharkiv, 61072, Ukrain.

M.K.Yankel Kharkov National University of Radio Electronics,

Lenin Ave.4, 61161, Kharkov Ukraine)


"Physical Methodology for Economic Systems Modeling”, EJTP 7, No. 24 (2010) 57–78. .and for his several innovative contributions to different Physics' areas Theoretical Physics.



The paper discusses the possibility of constructing economic models using the methodology of model construction in classical mechanics. At the same time, unlike the “econophysical” approach, the properties of economic models are derived without involvement of any equivalent physical properties, but with account of the types of symmetry existing in the economic system. It has been shown that at this approach practically all known mechanical variables have their “economic twins”. The variational principle is formulated on the basis of formal mathematical construction without involving the subjective factor common to the majority of models in economics. The dynamics of interaction of two companies has been studies in details, on the basis of which we can proceed to modeling of more complex and realistic economic systems. Prediction of the possibility of constructing economic theory on the basis of primary principles analogously to physics has been made.




EJTP Best Special Issue Paper 2010:


Robert carroll (Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801-2975 USA)


"Quantum potential as information: a mathematical survey", New trends in quantum information,  Aracne Editorice, Rome, Italy (2010) and for his major  contributions of different aspects of Mathematical Physics and Applied Mathematics..



We obtain transformation equations for the Bell basis states under an arbitrary Lorentz boost and compute the expectation values of the relativistic center of mass spin operator under each of these boosted states. We also obtain expectation values for spin projections along the axes.


2012 Majorana Prizes Laureates:


EJTP Best Person in Physics 2012:


Basil J. Hiley (Theoretical Physics Research Unit, Birkbeck, University of London, UK)


For his fundamentals contribution to Theoretical Physics, in particular for the Algebraic Approach to Quantum Mechanics which has made possible a deeper understanding of non-locality and the Quantum Mechanics and Quantum Field Theories' connections. In addition to his achievements, we want also to recognize his paramount importance as natural philosopher, his critical and open minded attitude towards the role of science in  contemporary culture.



“I would like to take this opportunity to formally acknowledge the considerable mathematical help I have received from Maurice de Gosson, Ernst Binz and Fabio Frescura without whose input my work would not have been possible.  I would also like to acknowledge the input of my colleagues Robert Callaghan, David Robson and Graham Yendall who have helped me clarify many difficult points that have cropped up over the years and above all the acknowledge the considerable input of David Bohm whose discussion have made my work possible”. B. J. Hiley.



EJTP Best Annual Paper 2012:


Yasuhito Kaminaga (Department of Mathematics, Gunma National College of Technology, Maebashi, Gunma, Japan)


For your Paper entitled "Covariant Analytic Mechanics with Differential Forms and Its Application to Gravity". EJTP 9, No. 26 (2012) 199–216.



We discuss fundamentals of the covariant analytic mechanics with differential forms. We apply it to typical field theories, such as a scalar field, the electromagnetic field, and a non-abelian gauge field, as well as the Newtonian mechanics of a harmonic oscillator. A significant feature of the covariant analytic mechanics is that the canonical equations, in addition to the Euler-Lagrange equation, are not only manifestly Lorentz covariant but also gauge covariant. In the latter half of the paper, we apply the covariant analytic mechanics to Einstein’s general theory of relativity, and show that the gravitational field can be successfully treated within the framework of it. We obtain the canonical equations of gravity with manifest diffeomorphism covariance





Majorana Prize committee (2012):


Erasmo Recami (Head of the Committee)

Fabio Majorana

E.C. George Sudarshan

Eliano Pessa

Jason Zimba

Leonardo Chiatti

José Luis Loَpez-Bonilla

Ignazio Licata

Ammar Sakaji

For suggestions and information: majorana[AT]ejtp.info






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