THE MODIFIED BARGMANN-WIGNER FORMALISM FOR HIGHER SPIN FIELDS AND RELATIVISTIC QUANTUM MECHANICS

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 and fermions. Connections with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2 S +1) theory are found. Next, we proceed to derive the 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 results we generalize the standard procedure and we obtain the spin-2 relativistic equations, which are consistent with the Einstein-Hilbert equation. We introduce the dual analogues of the Riemann tensor and we derive corresponding dynamical equations in the Minkowski space. Connections with the Marques-Spehler chiral gravity theory are discussed. The importance of the 4-vector field (and its gauge part) is pointed out. The spin-3/2 case is briefly discussed too.