On solution spaces of massless field equations with arbitrary spin

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.

Download Full-text

Invariance of the Massless Field Equations under Changes of the Metric

General Relativity and Gravitation ◽

10.1023/a:1018802624345 ◽

1998 ◽

Vol 30 (3) ◽

pp. 379-387 ◽

Cited By ~ 4

Author(s):

G. F. Torres del Castillo ◽

J. A. Mondragón-Sánchez

Keyword(s):

Field Equations ◽

Massless Field

Download Full-text

Uniﬁcation of massless ﬁeld equations solutions for any spin

EPL (Europhysics Letters) ◽

10.1209/0295-5075/ac4621 ◽

2021 ◽

Author(s):

Sergio Hojman ◽

Felipe Asenjo

Keyword(s):

Wave Equation ◽

Exact Solutions ◽

Potential Functions ◽

Field Equations ◽

Fermionic Field ◽

Massless Field ◽

Coupled Equations ◽

Klein Gordon ◽

Fermionic Fields ◽

Derivatives Of

Abstract A uniﬁcation in terms of exact solutions for massless Klein–Gordon, Dirac, Maxwell, Rarita– Schwinger, Einstein, and bosonic and fermionic ﬁelds of any spin is presented. The method is based on writing all of the relevant dynamical ﬁelds in terms of products and derivatives of pre–potential functions, which satisfy d’Alambert equation. The coupled equations satisﬁed by the pre–potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre–potentials that satisfy the usual wave equation which may be used to construct exact non–trivial solutions to Klein–Gordon, Dirac, Maxwell, Rarita–Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic ﬁeld equations, thus giving rise to an uniﬁcation of the solutions of all massless ﬁeld equations for any spin. Some solutions written in terms of orthogonal pre–potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

Download Full-text