Fermion-Fermion and Boson-Boson Amplitudes: Surprising Similarities

TL;DR

This paper compares boson-boson and fermion-boson interaction amplitudes calculated using a novel formalism in Lobachevsky space, revealing surprising similarities in their spin structures despite some differences.

Contribution

It introduces a comparison of boson-boson and fermion-boson amplitudes using Weinberg's formalism in Lobachevsky space, highlighting unexpected similarities.

Findings

Amplitudes exhibit similar spin structures in momentum transfer parametrization.

Differences between fermion and boson amplitudes are identified.

Potential physical applications of these similarities are discussed.

Abstract

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 by Skachkov long ago on the ground of the hamiltonian formulation of quantum field theory on the mass hyperboloid, $p_0^2 -{\vec p}^{2}=M^2$, 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.