Fundamental theories of waves and particles formulated without classical mass

Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called ‘wave mass’, which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.     

Relativistic non-instantaneous action-at-a-distance interactions

Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The Poincaré invariant parameters that label successive events along the world lines can be identified with the proper times of the particles provided that certain conditions are imposed on the interaction terms in the action. Further conditions on the interaction terms arise from the requirement that mass be a scalar. A generic class of theories with interactions that satisfy these conditions is found. The relativistic equations of motion for these theories are presented. We obtain exact circular orbits solutions of the relativistic one-body problem. The exact relativistic one-body Hamiltonian is also derived. The theory has three components: a linearly rising potential, a Coulomb-like interaction and a dynamical component to the Poincaré invariant mass. At the quantum level we obtain the generalized Klein–Gordon–Fock equation and the Dirac equation.     

On the theory of electron motion due to superposed em waves and its application to the free-electron laser with linear polarization

The relativistic motion of a charged particle in an electromagnetic field depending only on one coordinate is shown to be exactly equivalent to the unidimensional motion of a particle having a time and space-varying mass. By means of the averaged Lagrangian method an approximate solution is obtained for the relativistic electron motion in two oppositely moving waves of any polarization, one of them being weaker than the other one, thus generalizing the results previously obtained for circular polarization. A comparison with numerical calculations shows a good agreement. A pendulum-like motion in an effective periodic potential is shown to exist not only for two waves of the same frequency, but more generally when the frequency of the weaker wave is an odd harmonic of the frequency of the stronger one.This research was supported in part by CNR and the Italian Ministry of Education     

Influence of the Breit-Wigner type of instability on analytic properties of partial wave amplitudes

The relativistic binary processes are considered. For a general mass case the partial wave projection of an invariant amplitude involves some necessary continuation due to the appearance of the areas where the Mandelstam denominators vanish if the kinematical quantities have their physical values. To avoid the corresponding difficulties and to be able to perform practical and realistic calculations, the invariant amplitudes are expressed in terms of the exchanged stable and unstable objects and then they are projected onto the partial waves. In the present paper, their analytic properties in the complex energy squared plane are investigated in more detail. As the first approximation, the unstable objects are expressed in the Breit-Wigner form.     

Consistency of relativistic particle theories

While direct-interaction particle theories are generally thought to be incompatible with relativity in classical physics, such relativistic theories in quantum mechanics have recently attracted attention. The reasons for rejecting these theories in classical physics are based on the consideration of world lines, while relativistic quantum mechanics has no covariant position operator so that the classical refuting argument cannot be adapted.This paper discusses the consistency of relativistic particle theories with a finite number of degrees of freedom, without recourse to the position operator. A particle is described by a sub-algebra of observables at one time. Homogeneous transformations, including accelerations, must preserve the identity of particles, and therefore leave the sub-algebras invariant. It is shown that with this assumption only non-interacting particle theories are compatible with the principle of relativity, in quantum as well as classical mechanics.     

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example.     

Beltrami-de Sitter时空中标量和旋量粒子的量子理论

参照在Minkowski时空中,从粒子的相对论性经典理论过渡到量子理论,建立标量粒子和旋量粒子的相对论性波动方程的方案,在Beltrami-de Sitter时空中建立了de Sitter不变的标量粒子和旋量粒子的相对论性量子力学的基本方程,它们恰恰分别是Beltrami-de Sitter时空中的Klein-Gordon方程和Dirac方程。在Beltrami-anti de Sitter时空的同时类空超曲面簇上求解了这些方程,得到了分立的本征值和相应的本征函数。 关键词：     

A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

We study a fully relativistic, two-body, quadratic wave equation for equal mass interacting particles. With this equation the difficulties related to the use of the square roots in the kinetic energy operators are avoided. An energy-dependent effective interaction, also containing quadratic potential operators, is introduced. For pedagogical reasons, it is previously shown that a similar procedure can be also applied to the well-known case of a one-particle Dirac equation. The relationships of our model with other relativistic approaches are briefly discussed. We show that it is possible to write our equation in a covariant form in any reference frame. A generalization is performed to the case of two particles with different mass. We consider some cases of potentials for which analytic solutions can be obtained. We also study a general numerical procedure for solving our equation taking into account the energy-dependent character of the effective interaction. Hadronic physics represents the most relevant field of application of the present model. For this reason we perform, as an example, specific calculations to study the charmonium spectrum. The results show that the adopted equation is able to reproduce with good accuracy the experimental data.     

Nonlinear Behavior of Electromagnetic Waves in Ultra‐Relativistic Electron‐Positron Plasmas

A set of nonlinear equations which can self‐consistently describe the behavior of high frequency Electromagnetic (EM) waves in un‐magnetized, ultra‐relativistic electron‐positron (e‐p) plasmas is obtained on the basis of Vlasov‐Maxwell equations. Nonlinear wave‐wave, wave‐particle interactions lead to the coupling of high frequency EM waves with low frequency density perturbations which result from EM waves radiation pressure. The same as that in conventional electron‐ion (e‐i) plasmas, strong EM waves in e‐p plasmas will give rise to density depletion in which itself are trapped. But on the contrary to that in e‐i plasmas, there no longer exists electrostatic acoustic–like wave in e‐p plasmas due to the absence of mass difference. For linear polarized EM waves, a stationary EM soliton with a spiky structure will be formed. The possible relation of the localized field to pulsar radio pulse is discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relativistic study of electromagnetic electron cyclotron instability based on trapped electrons in kappa-Maxwellian auroral plasmas

The presence of relativistic electrons in the Earth's magnetosphere may excite EMEC waves via resonant interaction. The understanding of EMEC waves induced by such electrons requires relativistic treatment. Therefore, we present here the investigation of EMEC waves based on relativistic trapped electrons represented by kappa-Maxwellian distribution in auroral plasmas. The analytical expressions of real frequency and relativistic growth rate are derived. Our numerical outcomes report that relativistic approximation increases the wave growth and causes reduction in the threshold value of drift velocity of trapped electrons for instability. The wave frequency that corresponds to the maximum growth decreases as we go from nonrelativistic limit to relativistic. The maximum growth increases with the increment in plasma frequency, perpendicular thermal velocity, drift velocity of trapped electrons, and Lorentz factor γ. Moreover, the relativistic effects on maximum growth are more pronounced for smaller values of drift velocity and perpendicular thermal velocity.     

Review of invariant time formulations of relativistic quantum theories

The purpose of this paper is to review relativistic quantum theories with an invariant evolution parameter. Parametrized relativistic quantum theories (PRQT) have appeared under such names as constraint Hamiltonian dynamics, four-space formalism, indefinite mass, micrononcausal quantum theory, parametrized path integral formalism, relativistic dynamics, Schwinger proper time method, stochastic interpretation of quantum mechanics and stochastic quantization. The review focuses on the fundamental concepts underlying the theories. Similarities as well as differences are highlighted, and an extensive bibliography is provided.     

Studies of classical radiation emission from plasma wave undulators

The authors examine the characteristics of the classical radiation emitted by a relativistic electron beam that propagates perpendicularly through a large amplitude relativistic plasma wave. Such a study is useful for evaluating the feasibility of using relativistic plasma waves as extremely short wavelength undulators for generating short wavelength radiation. The electron trajectories in a plasma wave undulator are obtained using perturbation techniques and are then compared to numerical simulation results. The frequency spectrum and angular distribution of the spontaneous radiation emitted by a single electron and the stimulated radiation gain are obtained analytically, and are then compared to 3-D numerical simulations. The characteristics of the plasma wave undulator are compared to the AC free-electron laser (FEL) undulator and the conventional FEL     

A one-dimensional invariance principle for gauge fields of integer spin

A relativistic two-particle system is analyzed in which the particles are bound by an harmonic oscillator potential. The system is invariant under τ-reparametrizations as well as under two gauge transformations of the coordinates. The corresponding first-class constraints give a BRST charge which can be used to construct a classical field theory action for all integer spin gauge fields.     

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry (II)：—Higher Order Contributions

This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry" [Commun. Theor. Phys. 57 (2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R²-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.     

Macroscopic and mesoscopic matter waves

It has been shown earlier [3,6] that matter waves which are known to lie typically in the range of a few angstrom, can also manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This followed from the predictions of a probability amplitude theory by the author [1,2] in the classical macrodomain of the dynamics of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic situation whereby composite systems such as atoms and molecules in their highly excited internal states, can exhibit matter wave manifestation in macro and mesodomains, in one-dimensional scattering. The wave length of these waves is determined, not by the mass of the particle as in the case of the de Broglie wave, but by the frequency ω, of the classical orbital motion of the internal state in the correspondence limit, and is given by a nonquantal expression, λ = 2πv/ω, v being the velocity of the particle. For the electrons in a magnetic field the frequency corresponds to the gyrofrequency, Ω and the nonquantal wave length is given by λ = 2πv _|| /Ω; v _|| being the velocity of electrons along the magnetic field. Received 29 September 2001 / Received in final form 23 May 2002 Published online 19 July 2002     

Stochastic quantization method for spinning particles in a gravitational plane wave field

The exact and analytic Green functions for spinning relativistic particles in interaction with a gravitational plane wave field are obtained within the Stochastic Quantization Method of Parisi and Wu. We have separated the classical calculations from those related to the quantum fluctuations. The problem has been solved by using a perturbative treatment via the Langevin equation relying on phase and configuration spaces formulation.      

Classical and Quantum Theories of Spin

A great effort has been devoted to formulating a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in connecting classical and quantum theories rests in finding a parameter that plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneering works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level, we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail.     

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin–Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them θ-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing θ-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract θ-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein–Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as θ-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein–Gordon and Dirac equations in the noncommutative field theories. The θ-modified action of the relativistic spinning particle is just a generalization of the Berezin–Marinov pseudoclassical action for the noncommutative case.     

Noncommutative gravity, a ‘no strings attached’ quantum-classical duality, and the cosmological constant puzzle

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the ‘weakly quantum, strongly gravitational’ dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the ‘strongly quantum, weakly gravitational’ dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units. Second Award in the 2008 Essay Competition of the Gravity Research Foundation.