Generally relativistical Daffin-Kemmer formalis and behaviour of quantm-mechanical particle of spin 1 in the Abelian monopole field

TL;DR

This paper develops a generally relativistic Duffin-Kemmer formalism for spin 1 particles, analyzing their behavior in gravitational and Abelian monopole fields, highlighting the role of the Lorentz group and differences from Proca theory.

Contribution

It introduces a unified relativistic approach for spin 1 particles in curved spacetime using the Duffin-Kemmer formalism, emphasizing the Lorentz group's significance.

Findings

Constructed a generally relativistic Duffin-Kemmer equation.

Analyzed the behavior of spin 1 particles in Abelian monopole fields.

Highlighted the importance of the Lorentz group in the formalism.

Abstract

It is shown that the manner of introducing theinteraction between a spin 1 particle and external classical gravitational field can be successfully uni- fied with the approach that occurred with regard to a spin 1/2 particle and was first developed by Tetrode, Weyl, Fock, Ivanenko. On that way a general- ly relativistical Duffin-Kemmer equation is costructed. So, the manner of extending the flat space Dirac equation to general relativity case indicates clearly that the Lorentz group underlies equally both these theories. In other words, the Lorentz group retains its importance and significance at changing the Minkowski space model to an arbitrary curved space-time. In contrast to this, at generalizing the Proca formulation, we automatically destroy any relations to the Lorentz group, although the definition itself for a spin 1 particle as an elementary object was based on just this group. Such a gravity's sensitiveness to the fermion-boson division might appear rather strange and unattractive asymmetry, being subjected to the criticism. Moreover, just this feature has brought about a plenty of speculation on this matter. In any case, this peculiarity of particle-gravity field inter- action is recorded almost in every handbook. In the paper, on the base of the Duffin-Kemmer formalism developed, the problem of a vector particle in the Abelian monopole potential is considered.