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.

FRW viscous fluid cosmological model with time-dependent inhomogeneous equation of state

2017 ◽  
Vol 15 (01) ◽  
pp. 1830001 ◽  
Author(s):  
G. S. Khadekar ◽  
Deepti Raut
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Quadratic Form ◽  
State Parameter ◽  
The Other ◽  
Time Dependent ◽  
Inhomogeneous Equation ◽  
Field Equations ◽  
Equation Of State Parameter ◽  
Viscous Models

In this paper, we present two viscous models of non-perfect fluid by avoiding the introduction of exotic dark energy. We consider the first model in terms of deceleration parameter [Formula: see text] has a viscosity of the form [Formula: see text] and the other model in quadratic form of [Formula: see text] of the type [Formula: see text]. In this framework we find the solutions of field equations by using inhomogeneous equation of state of form [Formula: see text] with equation of state parameter [Formula: see text] is constant and [Formula: see text].

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.

PARADOXICAL KINEMATIC ACAUSALITY IN WEINBERG’S EQUATIONS FOR MASSLESS PARTICLES OF ARBITRARY SPIN

1992 ◽  
Vol 07 (22) ◽  
pp. 1967-1974 ◽  
Author(s):  
D.V. AHLUWALIA ◽  
D.J. ERNST
Keyword(s):  
Wave Equations ◽  
Classical Group ◽  
Arbitrary Spin ◽  
The Other ◽  
Finite Mass ◽  
Massless Particles ◽  
Paradoxical Situation ◽  
Other Hand ◽  
Free Particles

Weinberg’s equations for massless free particles of arbitrary spin are found to have acausal solutions. On the other hand, the m→0 limit of Joos-Weinberg’s finite-mass wave equations satisfied by (j, 0)⊕(0, j) j) covariant spinors are free from all kinematic acausality. This paradoxical situation is resolved and corrected by carefully studying the transition from the classical group theoretical arguments to quantum mechanically interpreted equations.

A wave equation for massive particles of arbitrary spin

1967 ◽  
Vol 297 (1450) ◽  
pp. 351-364 ◽  
Keyword(s):  
Wave Equation ◽  
Arbitrary Spin ◽  
Field Vector ◽  
Second Order ◽  
The Other ◽  
Particle Field ◽  
Gravitational Fields ◽  
Other Hand ◽  
Free Case ◽  
Unique Spin

A wave equation is given which, in the force-free case, describes a particle of unique spin and mass and which remains consistent when interactions are included. The equation is simple in the sense that it involves only matrices which satisfy the Pauli commutation rules. This simplicity is achieved at the expense of extending the particle field vector from one of 2j + 1 components to one of 4j. However, the extra 2j — 1 components are just what are needed to remove the inconsistency of the interacting system. In the force-free case these additional components vanish and the resulting equations are equivalent to the usual ones of Dirac, Fierz and Pauli. One the other hand, for the interacting system, the extra components do not vanish. The second order propagation equations are deduced in the case of external electromagnetic and gravitational fields.

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.

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