Antisymmetric Tensor Fields, 4-Vector Fields, Indefinite Metrics and Normalization

TL;DR

This paper extends the Dirac formalism to higher spins, explores dual tensor fields, and addresses indefinite metrics in quantization, connecting various theories in quantum field theory and gravity.

Contribution

It generalizes the Bargmann-Wigner formalism for higher spins to be compatible with other bosonic formalisms and clarifies indefinite metrics in 4-vector field quantization.

Findings

Relations with dual electrodynamics and the Ogievetskii-Polubarinov notoph established.

Derived dynamical equations for dual Riemann tensors in Minkowski space.

Clarified the role of indefinite metrics in quantizing 4-vector fields.

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(2J+1) theory are found. Next, 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 problem of indefinite metrics, particularly, in quantization of 4-vector fields is clarified.