Interactions of a $j=1$ boson in the $2(2j+1)$ component theory

TL;DR

This paper calculates interaction amplitudes for a spin-1 boson using the $2(2j+1)$ component formalism in Lobachevsky space, comparing results with earlier fermion interactions and discussing potential physical implications.

Contribution

It applies Weinberg's $2(2j+1)$ component formalism to boson interactions in Lobachevsky space and compares with prior fermion results, highlighting similarities and differences.

Findings

Boson-boson and fermion-boson amplitudes calculated in second-order perturbation theory.

Amplitudes exhibit similar spin structures but also notable differences.

Results have potential implications for understanding particle interactions in hyperbolic geometry.

Abstract

The amplitudes for boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the used model is the Weinberg's $2(2j+1)$ component formalism for describing a particle of spin $j$, recently developed substantially. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the ground of the hamiltonian formulation of quantum field theory on the mass hyperboloid, $p_0^2 -{\bf p}^2=M^2$, proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of $T$ matrices for the fermion and the boson cases. However, certain differences are found. Possible physical applications are discussed.