Poincar\'e Invariant Quantum Mechanics based on Euclidean Green functions

TL;DR

This paper presents a formulation of Poincaré invariant quantum mechanics utilizing Euclidean Green functions, enabling calculations of scattering, binding energies, and Poincaré transformations without analytic continuation, demonstrated through a toy model.

Contribution

It introduces a novel approach to Poincaré invariant quantum mechanics based on Euclidean Green functions, avoiding analytic continuation for computing physical observables.

Findings

Able to compute transition matrix elements up to 2 GeV

Demonstrates calculation of scattering and binding energies

Shows feasibility of finite Poincaré transformations

Abstract

We investigate a formulation of Poincar\'e invariant quantum mechanics where the dynamical input is Euclidean invariant Green functions or their generating functional. We argue that within this framework it is possible to calculate scattering observables, binding energies, and perform finite Poincar\'e transformations without using any analytic continuation. We demonstrate, using a toy model, how matrix elements of $e^{-\beta H}$ in normalizable states can be used to compute transition matrix elements for energies up to 2 GeV. We discuss some open problems.