Spin 1 Particle in a 15-Component Formalism, Interaction with Electromagnetic and Gravitational Fields
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex parameters $λ_{i}$, obeying two supplementary conditions, so restriction of the model to the case of electrically neutral vector particle is not a trivial task. A special basis in the space of 15-component wave functions is found where instead of four $λ_{i}$ only one real-valued quantity $σ$, a bilinear combination of $λ_{i}$, is presented. This $λ$-parameter is interpreted as an additional electromagnetic characteristic of a charged vector particle, polarizability. It is shown that in this basis $C$-operation is reduced to the complex conjugation only, without any accompanying linear transformation. Restriction to a massless vector particle is determined. Extension of the whole theory to the case of Riemannian space-time is accomplished. Two methods of obtaining corresponding generally covariant wave equations are elaborated: of tensor- and of tetrad-based ones. Their equivalence is proved. It is shown that in case of pure curved space-time models without Cartan torsion no specific additional interaction terms because of non-flat geometry arise. The conformal symmetry of a massless generally covariant equation is demonstrated explicitly. A canonical tensor of energy-momentum $T_{βα}$ is constructed, its conservation law happens to involves the Riemann curvature tensor. Within the framework of known ambiguity of any energy-momentum tensor, a new tensor $\bar{T}_{βα}$ is suggested to be used, which obeys a common conservation law.