scholarly journals The unitary representations of the Poincar\'e group in any spacetime dimension

2021 ◽  
Author(s):  
Xavier Bekaert ◽  
Nicolas Boulanger
Keyword(s):  
Arbitrary Dimension ◽  
Minkowski Spacetime ◽  
Irreducible Representations ◽  
Theoretical Treatment ◽  
Spacetime Dimension ◽  
Field Equations ◽  
Negative Mass ◽  
Relativistic Field ◽  
Fundamental Particles ◽  
Covariant Field

An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D\geqslant 3D≥3 is presented. An exhaustive treatment is performed of the two most important classes of unitary irreducible representations of the Poincar'e group, corresponding to massive and massless fundamental particles. Covariant field equations are given for each unitary irreducible representation of the Poincar'e group with non-negative mass-squared.

The Bianchi Identities in the Generalized Theory of Gravitation

1950 ◽  
Vol 2 ◽  
pp. 120-128 ◽  
Author(s):  
A. Einstein
Keyword(s):  
General Principle ◽  
Field Structure ◽  
Field Equations ◽  
Relativistic Field ◽  
Bianchi Identities ◽  
Principle Of Relativity ◽  
Dependent Variables ◽  
Physical Validity ◽  
Theory Of Gravitation

1. General remarks. The heuristic strength of the general principle of relativity lies in the fact that it considerably reduces the number of imaginable sets of field equations; the field equations must be covariant with respect to all continuous transformations of the four coordinates. But the problem becomes mathematically well-defined only if we have postulated the dependent variables which are to occur in the equations, and their transformation properties (field-structure). But even if we have chosen the field-structure (in such a way that there exist sufficiently strong relativistic field-equations), the principle of relativity does not determine the field-equations uniquely. The principle of “logical simplicity” must be added (which, however, cannot be formulated in a non-arbitrary way). Only then do we have a definite theory whose physical validity can be tested a posteriori.

Global dynamical time for binary point-like particle systems

2020 ◽  
Vol 17 (09) ◽  
pp. 2050131
Author(s):  
Osvaldo M. Moreschi
Keyword(s):  
Equations Of Motion ◽  
Minkowski Spacetime ◽  
Particle Systems ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Retarded Time ◽  
Dynamical Time ◽  
The Difference ◽  
Multiple Particle ◽  
Equations Of Motions

A geometrical construction for a global dynamical time for binary point-like particle systems, modeled by relativistic equations of motions, is presented. Thus, we provide a convenient tool for the calculation of the dynamics of recent models for the dynamics of black holes that use individual proper times. The construction is naturally based on the local Lorentzian geometry of the spacetime considered. Although in this presentation we are dealing with the Minkowskian spacetime, the construction is useful for gravitational models that have as a seed Minkowski spacetime. We present the discussion for a binary system, but the construction is obviously generalizable to multiple particle systems. The calculations are organized in terms of the order of the corresponding relativistic forces. In particular, we improve on the Darwin and Landau–Lifshitz approaches, for the case of electromagnetic systems. We discuss the possibility of a Lagrangian treatment of the retarded effects, depending on the nature of the relativistic forces. The higher-order contractions are based on a Runge–Kutta type procedure, which is used to calculate the quantities at the required retarded time, by increasing evaluations of the forces at intermediate times. We emphasize the difference between approximation orders in field equations and approximation orders in retarded effects in the equations of motion. We show this difference by applying our construction to the binary electromagnetic case.

scholarly journals TYPE II FLUID SOLUTIONS TO EINSTEIN'S FIELD EQUATIONS IN N-DIMENSIONAL SPHERICAL SPACETIMES

2002 ◽  
Vol 11 (01) ◽  
pp. 113-124 ◽  
Author(s):  
JAIME F. VILLAS Da ROCHA
Keyword(s):  
Black Holes ◽  
Large Class ◽  
Type Ii ◽  
Einstein Field Equations ◽  
Spacetime Dimension ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Naked Singularities ◽  
Type Ii Fluid

A large class of Type II fluid solutions to Einstein field equations in N-dimensional spherical spacetimes is found, wich includes most of the known solutions. A family of the generalized collapsing Vaidya solutions with homothetic self-similarity, parametrized by a constant λ, is studied, and found that when λ>λ c (N), the collapse always forms black holes, and when λ<λ c (N), it always forms naked singularities, where λ c (N) is function of the spacetime dimension N only.

Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation

2016 ◽  
Vol 71 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Friedwardt Winterberg
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Negative Energy ◽  
Quantum Mechanical ◽  
Field Equations ◽  
Negative Mass ◽  
Pilot Wave ◽  
Extended Theories Of Gravity

AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.

scholarly journals Component Minimization of the Bargmann?Wigner Wavefunction

1978 ◽  
Vol 31 (2) ◽  
pp. 137 ◽  
Author(s):  
EA Jeffery
Keyword(s):  
Arbitrary Spin ◽  
Spin Operator ◽  
The Other ◽  
Operator Matrices ◽  
Field Equations ◽  
Relativistic Field

The Bargmann-Wigner equations are used to derive relativistic field equations with only 2(2j+ 1) components of the original wavefunction. The other components of the Bargmann-Wigner wavefunction are superfluous and can be defined in terms of the 2(2j+ 1) components. The results are compared with various 2(2j+ 1) theories in the literature. Sylvester's theorem and some properties of induced matrices give simple relationships between the operator matrices of the field equations and the arbitrary spin operator matrices.

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