On the geometric and algebraic foundation of the spinor formalism and the application to relativistic field equations

1977 ◽  
Vol 16 (7) ◽  
pp. 533-540 ◽  
Author(s):  
W. Ulmer
Keyword(s):  
Field Equations ◽  
Relativistic Field ◽  
Algebraic Foundation ◽  
Spinor Formalism

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.

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.

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.

scholarly journals Relativistic field equations from higher-order polarizations of the poincaré group

1998 ◽  
Vol 41 (2) ◽  
pp. 193-202
Author(s):  
Miguel Navarro ◽  
Manuel Calixto ◽  
Víctor Aldaya
Keyword(s):  
Higher Order ◽  
Poincaré Group ◽  
Field Equations ◽  
Relativistic Field ◽  
Poincare Group

scholarly journals To Conserve, or Not to Conserve: A Review of Nonconservative Theories of Gravity

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 38
Author(s):  
Hermano Velten ◽  
Thiago R. P. Caramês
Keyword(s):  
Conservation Law ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Additional Constraint ◽  
Field Equations ◽  
Relativistic Field ◽  
Extended Theories Of Gravity ◽  
General Relativistic ◽  
Theories Of Gravity ◽  
Extended Theories

Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy–momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity allowing departures from the usual conservative framework. Many of these theories became popular in the last few years, aiming to describe the phenomenology behind dark matter and dark energy. However, within these scenarios, it is common to see attempts to preserve the conservative property of the energy–momentum tensor. Most of the time, it is done by means of some additional constraint that ensures the validity of the standard conservation law, as long as this option is available in the theory. However, if no such extra constraint is available, the theory will inevitably carry a non-trivial conservation law as part of its structure. In this work, we review some of such proposals discussing the theoretical construction leading to the non-conservation of the energy–momentum tensor.

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