Electronic Journal of Theoretical Physics

Open access journal for theoretical physics

ISSN 1729-5254

For Issues (1-6), please contact the editor at: info[AT]ejtp.com.

Volume 2, Issue 7 (August 2005)

Full text: Acrobat PDF (520 KB)

Number	Articles Title	Abstract
1	*Application of Coadjoint Orbits in the Thermodynamics of Non-Compact Manifolds.* V. V. Mikheyev; I. V. Shirokov Full text: Acrobat PDF (197 KB)	Method of the solution of the main problem of homogeneous spaces thermodynamics for non-compact spaces in the case of non-compact Lie groups is presented in the article. The method is based on the method of coadjoint orbits. The formula that allows efficiently evaluate heat kernel on non-compact spaces is obtained. The method is illustrated by non-trivial example.
2	*The Boundary Conditions Geometry in Lattice-Ising Model* You-gang Feng Full text: Acrobat PDF (126 KB)	We found that the differential topology of the lattice-system Ising model determines whether there can be the continuous phase transition, The geometric topology of the space the lattice-system is embedded in determines whether the system can become ordered. If the system becomes ordered it may not admit the continuous phase transition. The spin-projection orientations are strongly influenced by the geometric topology of the space the lattice system is embedded in.
3	*Simulation of Ginger EPR Spectra Obtained by X-Irradiation: Quantum Approach* S. Laachir; M. Moussetad; R. Adhiri; A. Fahli; M. Aboulfatah; M. Mikou Full text: Acrobat PDF (139 KB)	The ginger sample has been exposed to X-rays at cumulative doses. The foodstuffs irradiation is used in particular to improve their hygienic qualities and increase their shelf lives. This process has been approved by various international organizations: FAO -- AIEA -- WHO. In the present work, we propose to reproduce by simulation, based on a quantum approach, of the ESR (Electron Spin Resonance) spectra. The semi-classical approach is valid for a simple system, but not for a complex system such as an atom with hyperfine structure. In this case a quantum approach, based on spin Hamiltonian, is essential to interpret the ESR spectra. The main result is that the simulated spectra are in good agreement with the experimental ones obtained before and after irradiation.
4	*Quantum AdS¹⁺³ Black Holes with Effective Cosmological Constant* El-Nabulsi Ahmad Rami Full text: Acrobat PDF (249 KB)	A quantum AdS¹⁺³ massive and massless black holes with effective cosmological constant induced from non-minimal coupling and supergravities arguments are constructed and discussed in details.

Volume 2, Issue 8 (December 2005)

Full text: Acrobat PDF (704 KB)

Number	Articles Title	Abstract
1	*Fractional Unstable Euclidean Universe.* El-Nabulsi Ahmad Rami Full text: Acrobat PDF (174 KB)	Despite common acceptance of Big Bang hypothesis among most cosmologists, nonetheless there are criticisms from a small number of theorists partly supported by astronomy observation suggesting that redshift data could not always be attributed to cosmological expansion. In this paper, a new approach to cosmology fractional calculus has been developed that we hope will attract attention from astrophysicists and cosmologists because of the way it challenges the conventional big bang framework.
2	*Parametric Relationships Among Some Phenomenological Non-Relativistic Hadronic Potentials* Teik-Cheng Lim Full text: Acrobat PDF (153 KB)	In recent years, parametric relationships between interatomic potential energy functions have been developed in the realm of molecular chemistry and condensed matter physics. However, no parametric relationships have been developed so far among intra-atomic potentials. As an extension of previous works into the realm of intra-atomic potentials, we herein consider the possibility that hadronic potentials can be interrelated via their parameters. Hadronic potentials give quantitative description of interquark energy in terms of interquark distance, hence understanding how each potential function influences the theoretical modeling can be sought via knowledge of interrelationship amongst the potentials parameters. Phenomenological non-relativistic hadronic potentials are related amongst the mixed-powerlaw potential themselves, and with the Logarithmic potentials using calculus. Exact nonlinear relationships were obtained between the parameters whereby the interquark distance is included as one of the variables. It is also demonstrated that, when the interquark distance in the parametric relationships is assigned a fixed value of unity, the parametric relationships remain valid from the plotted potential energy curves..
3	*Non Linear Assessment of Musical Consonance* SLluis Lligo˜na Trulla, Alessandro Giuliani, Giovanna Zimatore, Alfredo Colosimo and Joseph P. Zbilut Full text: Acrobat PDF (326 KB)	The position of intervals and the degree of musical consonance can be objectively explained by temporal series formed by mixing two pure sounds covering an octave. This result is achieved by means of Recurrence Quantification Analysis (RQA) without considering neither overtones nor physiological hypotheses. The obtained prediction of a consonance can be considered a novel solution to Galileo's conjecture on the nature of consonance. It constitutes an objective link between musical performance and listeners hearing activity..
4	*Conditions for the Generation of Causal Paradoxes from Superluminal Signals* Giuseppe Russo Full text: Acrobat PDF (203 KB)	We introduce a simple method to illustrate how the Lorentz transformation lead to causal loop paradoxes when they are applied to superluminal velocities.

Volume 3, Issue 9 (February 2006)

Full text: Acrobat PDF (1,206 KB)

Number	Articles Title	Abstract
1	*Spinning of Particles in Schwarzschild-de-Sitter and Schwarzschild-Anti-de-Sitter Space-Times with `Effective Cosmological Constant'.* El-Nabulsi Ahmad Rami Full text: Acrobat PDF (132 KB)	Spinning of particles in SdS and SAdS space-times with effective cosmological constant is discussed in details. It is shown that the equilibrium conditions are independent of the spin of the test particles and are satisfied only for particular conditions relating the Einstein's cosmological constant with the ultra-light masses implemented in the theory from supergravities arguments and non-minimal coupling.
2	*How S-S' di Quark Pairs Signify an Einstein Constant Dominated Cosmology, and Lead to New Inflationary Cosmology Physics* A. W. Beckwith Full text: Acrobat PDF (335 KB)	We review the results of a model of how nucleation of a new universe occurs, assuming a di quark identification for soliton-anti soliton constituent parts of a scalar field. Initially, we employ a false vacuum potential system; however, when cosmological expansion is dominated by the Einstein cosmological constant at the end of chaotic inflation, the initial di quark scalar field is not consistent w.r.t a semi classical consistency condition we analyze as the potential changes to the chaotic inflationary potential utilized by Guth. We use Scherrer's derivation of a sound speed being zero during initial inflationary cosmology, and obtain a sound speed approaching unity ~as the slope of the scalar field moves away from a thin wall approximation. All this is to aid in a data reconstruction problem of how to account for the initial origins of CMB due to dark matter since effective field theories as presently constructed require a cut off value for applicability of their potential structure. This is often at the cost of, especially in early universe theoretical models, of clearly defined baryogenesis, and of a well defined mechanism of phase transitions.
3	*Vectorial Lorentz Transformations* Jorge A. Franco R. Full text: Acrobat PDF (403 KB)	We have noticed in relativistic literature that the derivation of Lorentz Transformations (LT) usually is presented by confining the moving system O' to move along the X-axis, namely, as a particular case of a more general movement. When this movement is generalized different transformations are obtained (which is a contradiction by itself) and a hidden vectorial characteristic of time is revealed. LT have been generalized in order to solve some physical and mathematical inconsistencies, such as the dissimilar manners (transversal, longitudinal) the particle's shape is influenced by its velocity and LT's inconsistency with Maxwell equations when in its derivation the pulse of light is sent perpendicular to the displacement of the moving system O'. Unlike the canonical derivation of LT, in the undertaken development of the generalized LT, assumptions were not used. Practical applications of generalized Vectorial Lorentz Transformations (VLT) were undertaken and as outcome a new definition of Local Lorentz Transformations (LLT) of magnitudes appeared. As another consequence, a characteristic and unique scaling Lorentz factor was obtained for each magnitude Given this, a dimensional analysis based upon these Lorentz factors came up. In addition, dynamical transformations were obtained and a new definition of mass was found.
4	*Lattice Dynamics of Hydrogen Interstice Co_{0.92}Fe_{0.08}* C. Kalai Arasi, R. John Bosco Balaguru, S. Alfred Cecil Raj, and N. Lawrence Full text: Acrobat PDF (465 KB)	Lattice dynamics of hydrogen interstice in the binary alloy Co_{0.92} Fe _{0.08} has been carried out to calculate the phonon dispersions along the [100], [110], [111] directions. The phonon density of states, variation of specific heat capacity and Debye's temperature with temperature are also calculated. A reasonably good agreement is found between the calculated and other theoretical and experimental results. The mean square displacement (MSD) of atoms surrounding the interstitial hydrogen atom is reported along with the defect modes.
5	*Petrov classification of the conformal tensor* M. A. Acevedo M., M. Enciso-Aguilar, and J. Lopez-Bonilla Full text: Acrobat PDF (110 KB)	We exhibit a flux diagram in its tensorial and Newman-Penrose representations for the Petrov classification.
6	*On Inflation Potentials in Randall-Sundrum Braneworld Model* M.Bennai, H.Chakir, and Z.Sakhi Full text: Acrobat PDF (168 KB)	We study the inflationary dynamics of the universe in the Randall-Sandrum typeII Braneworld model. We consider both an inverse-power law and exponential potentials and apply the Slow-Roll approximation in high energy limit to derive analytical expression of relevant inflationary quantities. An upper bound for the coupling constant was also obtained and a numerical value of perturbation spectrum is calculated in good agreement with observation.
7	*Considerations About The Anomalous Efficiency Of Particular Thermodynamic Cycles* Leonardo Chiatti Full text: Acrobat PDF (292 KB)	Some years ago Vignati (refs. 1, 2, 3) showed that, under some particular circumstances (inter alia isobaric processes connected through internal heat exchangers), the efficiency of an Ericsson cycle involving a real gas can exceed the Carnot limit \eta_{C} , in contradiction with the second principle of thermodynamics. However, the convergence of Vignati's algorithm, giving the temperature difference between the intermediate heat exchangers, has not yet been proved. In particular, it isn't clear, if the number of intermediate heat exchangers infinitely increases, the condition of a total (perfect) heat recovery may be asymptotically approximated. This remark is relevant because the claimed anomalous efficiencies appear only in the limit of a perfect heat recovery. Considering a suitable counterexample, we prove that, in general, the residual heat discharged on the external sources does not vanish in that limit, even when the isobars exchange the same amount of heat. Therefore the violation of the second law inferred from Vignati's calculation is merely apparent, being referred to a situation which is not (in principle) physically realisable. The essentials of the Vignati's argument are then applied to an Ericsson cycle involving an ideal gas undergoing chemical reactions. Again, no contradiction arises with the second principle.

Volume 3, Issue 10 (April 2006), Majorana Issue (Editor: Ignazio Licata)

Full text: Acrobat PDF (1,988 KB)

Number

Articles Title

Abstract

Majorana Imoact on Contemporary Physics

Ignazio Licata

Full text: Acrobat PDF (14 KB)

Editorial Note

The Scientific Work Of Ettore Majorana: An Introduction

Erasmo Recami

Full text: Acrobat PDF (113 KB)

A Brief bibliography of the scientific work of Ettore Majorana has been discussed.

On the Hamiltonian Form of Generalized Dirac Equation for Fermions with Two Mass States

Sergey. I. Kruglov

Full text: Acrobat PDF (126 KB)

Dynamical and non-dynamical components of the 20-component wave function are separated in the generalized Dirac equation of the first order, describing fermions with spin 1/2 and two mass states. After the exclusion of the non-dynamical components, we obtain the Hamiltonian Form of equations. Minimal and non-minimal electromagnetic interactions of particles are considered here.

Majorana Equation and exotics: Higher Derivative Models, Anyons and Noncommutative Geometry

Mikhail S. Plyushchay

Full text: Acrobat PDF (199 KB)

In 1932 Ettore Majorana proposed an infinite-component relativistic wave equation for particles of arbitrary integer and half-integer spin. In the late 80s and early 90s it was found that the higher-derivative geometric particle models underlie the Majorana equation, and that its (2+1)-dimensional analogue provides with a natural basis for the description of relativistic anyons. We review these aspects and discuss the relationship of the equation to the exotic planar Galilei symmetry and noncommutative geometry. We also point out the relation of some Abelian gauge field theories with Chern-Simons terms to the Landau problem in the noncommutative plane from the perspective of the Majorana equation.

Wave Equations, Renormalization and Meaning of the Planck's Mass: Some Qualitative Considerations

Leonardo Chiatti

Full text: Acrobat PDF (131 KB)

The five-dimensional version of the quantum relativistic Klein-Gordon wave equation is assumed to be a more fundamental description for the dynamics of the single particle without spin. The meaning of the renormalization procedure in QFT and the Planck's mass one are briefly discussed from this point of view.

Nonlinear Field Equations and Solitons as Particles

Attilio Maccari

Full text: Acrobat PDF (346 KB)

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

The Quantum Character of Physical Fields.

Foundations of Field Theories

Ludmila. I. Petrova

Full text: Acrobat PDF (161 KB)

The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one has to know how such closed exterior forms are obtained. In the present paper it is shown that closed exterior forms corresponding to field theories are obtained from the equations modeling conservation (balance) laws for material media. It has been developed the evolutionary method that enables one to describe the process of obtaining closed exterior forms. The process of obtaining closed exterior forms discloses the mechanism of evolutionary processes in material media and shows that material media generate, discretely, the physical structures, from which the physical fields are formed. This justifies the quantum character of field theories. On the other hand, this process demonstrates the connection between field theories and the equations for material media and points to the fact that the foundations of field theories must be conditioned by the properties of material media. It is shown that the external and internal symmetries of field theories are conditioned by the degrees of freedom of material media. The classification parameter of physical fields and interactions, that is, the parameter of the unified field theory, is connected with the number of noncommutative balance conservation laws for material media.

Relativistic Causality and

Quasi -Orthomodular Algebras

Renato.Nobili

Full text: Acrobat PDF (218 KB)

The concept of fractionability or decomposability in parts of a physical system has its mathematical counterpart in the lattice--theoretic concept of orthomodularity. Systems with a finite number of degrees of freedom can be decomposed in different ways, corresponding to different groupings of the degrees of freedom. The orthomodular structure of these simple systems is trivially manifest. The problem then arises as to whether the same property is shared by physical systems with an infinite number of degrees of freedom, in particular by the quantum relativistic ones. The latter case was approached several years ago by Haag and Schroer (1962; Haag, 1992) who started from noting that the causally complete sets of Minkowski spacetime form an orthomodular lattice and posed the question of whether the subalgebras of local observables, with topological supports on such subsets, form themselves a corresponding orthomodular lattice. Were it so, the way would be paved to interpreting spacetime as an intrinsic property of a local quantum field algebra. Surprisingly enough, however, the hoped property does not hold for local algebras of free fields with superselection rules. The possibility seems to be instead open if the local currents that govern the superselection rules are driven by gauge fields. Thus, in the framework of local quantum physics, the request for algebraic orthomodularity seems to imply physical interactions! Despite its charm, however, such a request appears plagued by ambiguities and criticities that make of it an ill--posed problem. The proposers themselves, indeed, concluded that the orthomodular correspondence hypothesis is too strong for having a chance of being practicable. Thus, neither the idea was taken seriously by the proposers nor further investigated by others up to a reasonable degree of clarification. This paper is an attempt to re--formulate and well--pose the problem. It will be shown that the idea is viable provided that the algebra of local observables: (1) is considered all over the whole range of its irreducible representations; (2) is widened with the addition of the elements of a suitable intertwining group of automorphisms; (3) the orthomodular correspondence requirement is modified to an extent sufficient to impart a natural topological structure to the intertwined algebra of observables so obtained. A novel scenario then emerges in which local quantum physics appears to provide a general framework for non--perturbative quantum field dynamics.

Lorentz Invariant Majorana Formulation of Electrodynamics in the Clifford Algebra Formalism

Tomislav Ivezic

Full text: Acrobat PDF (143 KB)

In this paper we present a new geometric formulation (Clifford algebra formalism) of the field equations, which is independent of the reference frame and of the chosen system of coordinates in it. This formulation deals with the complex 1-vector \Psi =E-icB (i is the unit imaginary), which is four-dimensional (4D) geometric generalization of Majorana's complex 3D quantity \Psi }=E-icB. When the sources are absent the field equations with the complex \Psi become Dirac-like relativistic wave equations for the free photon. In the frame of ``fiducial'' observers (the observers who measure fields are at rest) and in the standard basis the component form of the field equations with 4D \Psi reproduces the component form of Majorana-Maxwell equations with 3D field \Psi . The important differences between the approach with the 4D \Psi and that one with the 3D \Psi are discussed.

" Anticoherent " Spin States via the Majorana Representation

Jason Zimba

Full text: Acrobat PDF (400 KB)

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.

Stretching the Electron as Far as it Will Go

G. W. Semenoff and P. Sodano

Full text: Acrobat PDF (287 KB)

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.

Why do Majorana Neutrinos Run Faster than Dirac Neutrinos?

Zhi-zhong Xing and He Zhang

Full text: Acrobat PDF (380 KB)

The \tau-lepton dominance in the one-loop renormalization-group equations (RGEs) of neutrinos sets a cute criterion to parametrize the 3x3 lepton flavor mixing matrix U: its elements U_{3i} (for i=1,2,3) should be as simple as possible. Such a novel parametrization is different from the ``standard" one used in the literature and can lead to greatly simplified RGEs for three mixing angles and the physical CP-violating phase(s), no matter whether neutrinos are Dirac or Majorana particles. We show that the RGEs of Dirac neutrinos are not identical with those of Majorana neutrinos even if two Majorana CP-violating phases vanish. As the latter can keep vanishing from the electroweak scale to the typical seesaw scale, it makes sense to explore the similarities and differences between the RGE running effects of Dirac and Majorana neutrinos. We conclude that Majorana neutrinos are in general expected to run faster (i.e., more significantly) than Dirac neutrinos.

Universe Without Singularities

A Group Approach to De Sitter Cosmology

Ignazio Licata

Full text: Acrobat PDF (162 KB)

In the last years the traditional scenario of ``Big Bang'' has been deeply modified by the study of the quantum features of the Universe evolution, proposing again the problem of using ``local'' physical laws on cosmic scale, with particular regard to the cosmological constant role. The ``group extention'' method shows that the De Sitter group univocally generalizes the Poincaré group, formally justifies the cosmological constant use and suggests a new interpretation for Hartle-Hawking boundary conditions in Quantum Cosmology.

Majorana and the Investigation of Infrared Spectra of Ammonia

Elisabetta. Di Grezia

Full text: Acrobat PDF (169 KB)

An account is given on the first studies on the physics of ammonia, focusing on the infrared spectra of that molecule. Relevant contributions from several authors, in the years until 1932, are pointed out, discussing also an unknown study by E.Majorana on this topic.

Exact Solution of Majorana Equation via Heaviside Operational Ansatz

Valentino A. Simpao

Full text: Acrobat PDF (215 KB)

In context of a transformation between Majorana and Dirac wavefunctions, it suffices to solve the related interactive Dirac problem and then apply the transformation of variables on the Dirac wavefunction in order to obtain the Majorana wavefunction of the given Majorana equation. Clearly, this connection between solutions continues to hold if the free Majorana and Dirac equations are each coupled to an external gauge field [e.g., Electromagnetism] via the minimum coupling prescription. Applying the formal solution scheme Heaviside Operational Ansatz[heretofore, HOA] put forward in [ EJTP 1 (2004), 10-16], provides an exact quadrature solution for the massive minimum-coupled Majorana equation in terms of the solution of the corresponding massive minimum-coupled Dirac equation.

A Logical Analysis of Majorana’s Papers on Theoretical Physics

A. Drago and S. Esposito

Full text: Acrobat PDF (161 KB)

We study two celebrated Majorana's papers through a method of investigation which relies upon the recently recognized distinction between classical logic and several kinds of non-classical logics, i.e. the failure of the double negation law. This law fails when a double negated sentence is not equivalent to the corresponding positive sentence, owing to the lack of scientific evidence of the latter one. All recognized double negated sentences inside the text of each paper are listed; the mere sequence of such sentences giving the logical thread of Majorana's arguing. This one is recognized to be of the Lagrangian kind, which mixes logical arguing and mathematical calculation; i.e. the author puts a fundamental problem which is solved by anticipating the mathematical hypothesis able to solve it, and then by drawing from this hypothesis the mathematical consequences in order to reach to desired result. Furthermore the rethoric of presentation used by Majorana results to be a juridical one, owing to his style of presenting the laws to which an ideal theoretical physicist has to conform his mind in order to solve the problem at issue.

Four Variations on Theoretical Physics by Ettore Majorana

Salvatore. Esposito

Full text: Acrobat PDF (219 KB)

An account is given of some topical unpublished work by Ettore Majorana, revealing his very deep intuitions and skillfulness in Theoretical Physics. The relevance of the quite unknown results obtained by him is pointed out as well.

The Majorana Oscillator

Eliano Pessa

Full text: Acrobat PDF (124 KB)

At present the expression ‘Majorana oscillator’ does not appear to be in use in theoretical physics. However, the author of this paper heard it in the Seventies, during private conversations with the late Prof. B.Touschek. This little contribution tries to explore the possible meanings of this expression and introduces a new field equation, generalizing the one already introduced by Majorana himself, which could describe a hypothetical ‘Majorana oscillator’.

Scattering of an \alpha Particle by a Radioactive Nucleus

Unpublished 1928

Ettore Majorana

Full text: Acrobat PDF (166 KB)

In the following we reproduce, translated into English, a section of Volumetto II, a notebook written by Majorana in 1928 when he was still a Physics student at the University of Rome (see S. Esposito, E. Majorana jr, A. van der Merwe and E. Recami (eds.) Ettore Majorana: Notes on Theoretical Physics, Kluwer, New York, 2003). This study was performed by the author when he was preparing his Thesis work on ``The Quantum Theory of Radioactive Nuclei'' (unpublished), whose supervisor was E. Fermi.

S. Esposito

Comments on a Paper by Majorana Concerning Elementary Particles

David. M. Fradkin

Full text: Acrobat PDF (145 KB)

An early paper (1932) by Majorana, that has received but scant attention, is reexamined in light of later developments. This pioneering paper constructs a relativistically invariant theory of arbitrary spin particles, develops and utilizes infinite dimensional representations of the homogeneous Lorentz group, and provides a mass spectrum for elementary particles. The relevance of Majorana’s approach and results to later and current research is explained.

We reproduce here the historical D. M. Fradkin 1966 paper whose role among the physicists of high energy was decisive; since then espressions like "Majorana mass", "Majorana spinors" and "Majorana neutrino" have become usual. The paper is based upon the work Teoria di Particelle con Momento Intrinseco Arbitrario, translated by Italiam from Edoardo Amaldi.