Notoph-Graviton-Photon Coupling

TL;DR

This paper develops a unified quantum field theory framework for photon, notoph, and graviton fields using the Bargmann-Wigner formalism, linking higher spin theories with general relativity and exploring their interactions.

Contribution

It introduces a modified Bargmann-Wigner approach to describe photon, notoph, and graviton within a single formalism, deriving consistent relativistic equations for these fields.

Findings

Unified description of photon, notoph, and graviton fields.

Derived relativistic equations consistent with general relativity.

Estimated possible interactions among these fields.

Abstract

In the sixties Ogievetskii and Polubarinov proposed the concept of a notoph, whose helicity properties are complementary to those of a photon. Later, Kalb and Ramond (and others) developed this theoretical concept. And, at the present times it is widely accepted. We analyze the quantum theory of antisymmetric tensor fields with taking into account mass dimensions of notoph and photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive 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 general relativity. The importance of the 4-vector field (and its gauge part) is pointed out. Thus, we present the full theory which contains photon, notoph (the Kalb-Ramond field) and the graviton. The relations of this theory with the higher spin theories are established. In fact, we deduced the gravitational field equations from relativistic quantum mechanics. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph. PACS number: 03.65.Pm, 04.50.-h, 11.30.Cp