Fermion-fermion and boson-boson amplitudes: surprising similarities

TL;DR

This paper calculates and compares fermion-fermion, boson-boson, and fermion-boson interaction amplitudes in Lobachevsky space, revealing surprising similarities in their spin structures despite some differences, with potential physical implications.

Contribution

It demonstrates that fermion and boson amplitudes share similar spin structures when parametrized by momentum transfer in Lobachevsky space, highlighting unexpected parallels.

Findings

Fermion and boson amplitudes have similar spin structures.

Differences between fermion and boson amplitudes are identified.

The approach uses Weinberg's formalism and Lobachevsky space parametrization.

Abstract

Amplitudes for fermion-fermion, boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the model is the Weinberg's 2(2j+1)-component formalism for describing a particle of spin j. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the basis of the Hamiltonian formulation of quantum field theory on the mass hyperboloid, p_0^2 - 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 case and the boson case. However, certain differences are found. Possible physical applications are discussed.