The Bargmann-Wigner Formalism for Higher Spins (up to 2)

TL;DR

This paper generalizes the Bargmann-Wigner formalism for higher spins up to 2, establishing connections with dual electrodynamics, deriving consistent spin-2 equations, and discussing implications for chiral gravity and gauge fields.

Contribution

It introduces a modified formalism compatible with other bosonic theories, derives new spin-2 equations, and explores their relations with dual theories and gravity models.

Findings

Derived consistent relativistic equations for spin-2 fields.

Established relations with dual electrodynamics and chiral gravity.

Highlighted the role of the 4-vector gauge field.

Abstract

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2S+1) theory are found. Next, we proceed to derive the equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the previous one. We introduce the dual analogues of the Riemann tensor and derive corresponding dynamical equations in the Minkowski space. Relations with the Marques-Spehler chiral gravity theory are discussed. The importance of the 4-vector field (and its gauge part) is pointed out.