The Modified Bargmann-Wigner Formalism: Longitudinal Fields, Parity and All That

Abstract

In the old papers of Ogievetskii and Polubarinov, Hayashi, Kalb and Ramond the {\it notoph} concept, the longitudinal field originated from the antisymmetric tensor, has been proposed. In our work we analyze the theory of antisymmetric tensor field of the second rank from a viewpoint of the normalization problem. We obtain the 4-potentials and field strengths, which coincide with those which have been previously obtained in the works of Ahluwalia and Dvoeglazov. Slightly modifying the Bargmann-Wigner field function we conclude that it is possible to describe explicitly the degrees of freedom of the photon and of the {\it notoph} by the same equation. The physical consequences, such as parity properties of field functions, are discussed, relations to the previous works are discussed as well. Moreover, we derive equations for {\it symmetric} tensor of the second rank on the basis of the same modification of the Bargmann-Wigner formalism, i.e. the equations which describe dynamical behavior of the fields of maximal spin 2.