On conserved quantities in the theory of charged boson fields of spin 0 and 1

TL;DR

This paper derives conservation laws for charged boson fields of spin 0 and 1 using Dirac-Kahler theory, identifying known and new conserved quantities, including some with unclear physical meaning.

Contribution

It introduces a method to obtain conservation laws for bosons of different spins by imposing conditions on Dirac-Kahler fields, revealing new conserved currents.

Findings

Conserved charge vector j^{a}(x) identified for bosons.

Energy-momentum tensor T^{ab}(x) derived.

Additional conserved currents u^{a}(x) and u^{ab}(x) found for complex fields.

Abstract

Bosons of spin 0 and 1, with different intrinsic parities, are described by full sets of spinor equations in the frame of the Dirac-Kahler theory. This enables us to obtain the conservation laws for the boson particles with one value of spin by imposing linear additional conditions in the known sixteen conserved currents of the Dirac-Kahler field. In this way for each boson the known conserved quantities, charge vector j^{a}(x), symmetrical energy-momentum tensor T^{ab(x), and angular moment tensor L^{a[bc]}(x), have been found. Additionally, for scalar fields, one conserved current \nu^{a}(x) has been constructed; it is not zero one only for a complex-valued field. For a vector particles, two additional currents, \nu^{a}(x) and \nu^{ab}(x), are found that again do not vanish when fields are complex-valued. Those currents \nu^{a}(x) and \nu^{ab}(x) have not seemingly any physical interpretation.