The modified Bargmann-Wigner formalism: The Higher Spins

TL;DR

This paper extends the Bargmann-Wigner formalism to describe higher spin fields, including the photon and notoph, by analyzing the antisymmetric tensor field and deriving equations for spin-2 fields.

Contribution

It introduces a modified Bargmann-Wigner approach to explicitly describe photon and notoph degrees of freedom and derives equations for maximal spin 2 fields.

Findings

Consistent description of photon and notoph degrees of freedom.

Derived equations for spin-2 tensor fields.

Connected the formalism to previous works on antisymmetric tensor fields.

Abstract

In the old articles of Ogievetskii and Polubarinov, Kalb and Ramond the notoph concept, the longitudinal field originated from the antisymmetric tensor (AST), has been proposed. In our work we analyze the theory of the AST field of the second rank from the viewpoint of the normalization problem. We obtain 4-potentials and strengths which coincide with those obtained in the works of Ahluwalia and Dvoeglazov. We conclude that it is possible to describe degrees of freedom of the photon and of the notoph explicitly by slightly modified Bargmann-Wigner field function. The physical consequences and relations to the previous works are discussed. Furthermore, we derive equations for the symmetric tensor of the second rank on the basis of the same modification of the Bargmann-Wigner formalism, i.e., the equations which describe the dynamical behavior of the field of the maximal spin 2.