Scattering in a Euclidean formulation of relativistic quantum mechanics

TL;DR

This paper presents a Euclidean formulation of relativistic quantum mechanics that allows direct calculation of scattering observables without analytic continuation, demonstrated through a toy model.

Contribution

It introduces a Euclidean space-time based framework for relativistic quantum mechanics, enabling direct scattering calculations and avoiding analytic continuation.

Findings

Feasibility of direct scattering calculations demonstrated with a toy model

Representation of Hilbert space and Poincaré generators in Euclidean variables

Potential for simplifying relativistic quantum computations

Abstract

A Euclidean formulation of relativistic quantum mechanics is discussed. Representations of the Hilbert space inner product and Poincar\'e generators are all expressed in terms of Euclidean space-time variables. The formulation does not require analytic continuation and can be used to directly calculate scattering observables. A toy model is used to demonstrate the feasibility of performing scattering calculations using the suggested computational methods.