On algebraic models of relativistic scattering

TL;DR

This paper introduces an algebraic method for constructing relativistic scattering models using group theory, specifically relating the interacting mass operator to Casimir operators, with applications to SO(3,1) symmetry.

Contribution

It develops a novel algebraic approach linking the mass operator to Casimir operators within direct-interaction relativistic models.

Findings

Successfully relates the mass operator to Casimir operators of a non-compact group.

Derives the S matrix from intertwining relations of group representations.

Applies the method explicitly to a model with SO(3,1) symmetry.

Abstract

In this paper we develop an algebraic technique for building relativistic models in the framework of direct-interaction theories. The interacting mass operator M in the Bakamjian-Thomas construction is related to a quadratic Casimir operator C of a non-compact group G. As a consequence, the S matrix can be gained from an intertwining relation between Weyl-equivalent representations of G. The method is illustrated by explicit application to a model with SO(3,1) dynamical symmetry.