Theory of Antisymmetric Tensor Fields

TL;DR

This paper challenges the view that second-rank antisymmetric tensor fields are purely longitudinal after quantization, proposing a correct quantization approach that clarifies their physical properties and connections to gauge theories.

Contribution

It demonstrates a proper quantization method for antisymmetric tensor fields, clarifies their dynamical invariants, and discusses their relation to gauge theories, addressing longstanding misconceptions.

Findings

Correct quantization allows non-zero Pauli-Lubanski vector

Various forms of Proca equations can be derived

Connection between antisymmetric tensor fields and gauge theories is clarified

Abstract

It has long been claimed that the antisymmetric tensor field of the second rank is pure longitudinal after quantization. In my opinion, such a situation is quite unacceptable. I repeat the well-known procedure of the derivation of the set of Proca equations. It is shown that it can be written in various forms. Furthermore, on the basis of the Lagrangian formalism I calculate dynamical invariants (including the Pauli-Lubanski vector of relativistic spin for this field). Even at the classical level the Pauli-Lubanski vector can be equal to zero after applications of well-known constraints. The importance of the normalization is pointed out for the problem of the description of quantized fields of maximal spin 1. The correct quantization procedure permits us to propose a solution of this puzzle in the modern field theory. Finally, the discussion of the connection of the Ogievetskii-Polubarinov-Kalb-Ramond field and the electrodynamic gauge is presented.