Symmetries of the Relativistic Two-Boson System in?External Field

We investigate the survival of symmetries in a relativistic system of two mutually interacting bosons coupled with an external field, when this field is “strongly” translation invariant in some directions and additionally remains unchanged by other isometries of spacetime. Since the relativistic interactions cannot be composed additively, it is not a priori garanteed that the two-body system inherits all the symmetries of the external potential. However, using an ansatz which permits to preserve the compatibility of the mass-shell constraints in the presence of the field, we show how the “surviving isometries” can actually be implemented in the two-body wave equations.     

Symmetries of the Relativistic Two-Particle Model with Scalar-Vector Interaction

Abstract

A relativistic two-particle model with superposition of time-asymmetric scalar and vector interactions is proposed and its symmetries are considered. It is shown that first integrals of motion satisfy nonlinear Poisson-bracket relations which include the Poincaré algebra and one of the algebras so(1,3), so(4) or e(3).     

Geometrizing Relativistic Quantum Mechanics

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.     

Relativistic Mechanics of Continuous Media

In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an inviscid fluid we derive an analogue of the Bernoulli equation. For irrotational flow we prove that the velocity field can be derived from a potential. If in addition, the fluid is incompressible, the potential must obey the d'Alembert equation, and thus the problem is reduced to solving the d'Alembert equation with specific boundary conditions (in both space and time). The solutions indicate the existence of light velocity sound waves in an incompressible fluid (a result known in previous literature ⁽¹⁹⁾ ). Relaxing the constraints and allowing the fluid to become linearly compressible one can derive a wave equation, from which the sound velocity can again be computed. For a stationary background flow, it has been demonstrated that the sound velocity attains its correct values for the incompressible and nonrelativistic limits. Finally viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid.     

Nonlocality in Relativistic Dynamics

Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative interpretations of nonlocality.     

Time Operator in Relativistic Quantum Mechanics

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but nonzero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.     

Cluster Separability in Relativistic Quantum Mechanics

Using a simple model we provide a quantitative study of the size of the corrections needed to restore cluster properties to the construction of Poincaré invariant dynamical models with kinematic spins, first provided by B. Bakamjian and L. H. Thomas. Our model calculations suggest that these corrections are too small to have a quantitative impact on nuclear physics observables calculated using models with meson and nucleon degrees of freedom.     

Quantum Solutions in Relativistic Classical Mechanics

Russian Physics Journal - Quantum solutions of the classical equation of relativistic mechanics have been found. A synthesis of classical and quantum physics can become a basic formalism for a...     

Systems of Covariance in Relativistic Quantum Mechanics

Developing some earlier work for spin-zerosystems found in the literature, we use some recentlyobtained generalized systems of covariance for thePoincare group to suggest a method for definingcovariant localization operators on phase space formassive relativistic particles with arbitrary integralor half-integral spins. These operators lead tooperationally defined position operators on spacelikehyperplanes, which turn out to be the Newton-Wigneroperators, and, as in the earlier results on spin-zerosystems, admit a consistent probability interpretationwith conserved currents.     

Relativistic Quantum Mechanics and the Bohmian Interpretation

No Heading Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role, provides a viable interpretation of relativistic quantum mechanics. We formulate the Bohmian interpretation of many-particle wave functions in a Lorentz-covariant way. In contrast with the nonrelativistic case, the relativistic Bohmian interpretation may lead to measurable predictions on particle positions even when the conventional interpretation does not lead to such predictions.     

Geometric Quantization of Relativistic Hamiltonian Mechanics

A relativistic Hamiltonian mechanical system is seen as a conservative Dirac constraint system on the cotangent bundle of a pseudo-Riemannian manifold. We provide geometric quantization of this cotangent bundle where the quantum constraint serves as a relativistic quantum equation.     

Quantum Potential in Relativistic Dynamics

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential.     

Relativistic Dynamics in Basic Chemistry

This paper revisits the historical sequence in which some of the major developments of 20th-century physics occurred, and explores how theories could have turned out differently, if the sequence of developments had been different. It shows how a delay in founding special relativity theory until after (1) at least one puzzling problem in electromagnetic theory could be acknowledged, and (2) sat least some of the experimental observations pertinent to the development of quantum mechanics had become well known, could have resulted in a larger theory that covers both domains in a manner quite different from that of any of the theories we use today. The revised theory dispenses with a separate postulate introducing Planck’s constant h, identifying instead a physical mechanism that implies the constant. Some important aspects of quantum chemistry then follow. Editor, Galilean Electrodynamics, Proceedings of the Natural Philosophy Alliance; Visiting Industry Professor, Tufts University, retired     

Mei Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.     

Relativistic Quantum Mechanics as a Telegraph

A derivation by Fröhner of non-relativistic quantum mechanics via Fourier analysis applied to probability theory is not extendable to relativistic quantum mechanics because Schrödinger's positive definite probability density * is lost (Dirac's spin 1/2 case being the exception). The nature of the Fourier link then changes; it points to a redefinition of the probability scheme as an information carrying telegraph, the code of which is Born's as extended by Dirac and by Feynman. Hermitian symmetry of the transition amplitude between Dirac representations expresses reciprocity of preparation and measurement (the quantal coding and decoding), two equally active interventions of the physicist; as the measurement perturbs the system retrodiction implies retroaction evidenced in delayed choice. Reciprocity of knowledge and organization vindicates Wigner's claim that reciprocal to the action of matter upon mind there exists a direct action of mind upon matter: psychokinesis, branded by Jaynes as a psychiatric disorder of the Copenhagen school. As for factlike irreversibility, it is expressed by the enormity of the change rate from information to negentropy: while gain in knowledge is normal psychokinesis is paranormal. Stapp's recent discussion of psychokinesis in a quantum context should be resumed in association with an EPR correlation; an experimental test is proposed.     

Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems

Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D‘Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.     

Relativistic Quantum Mechanics and Field Theory

The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality property and the gauge invariance encoded in the Gauss' law is discussed in connection with the various quantization choices for gauge fields.