Euclidean Relativistic Quantum Mechanics

TL;DR

This paper presents a Poincaré invariant quantum mechanics framework based on Euclidean Green functions, detailing model construction, state representation, and transition matrix elements, with a simple model demonstrating feasibility.

Contribution

It introduces a novel formulation of relativistic quantum mechanics using Euclidean Green functions as input, emphasizing model construction and Poincaré invariance.

Findings

Feasibility demonstrated with a simple model

Constructed Hilbert space and single-particle states

Established transformation properties and transition matrix elements

Abstract

We discuss a formulation of exactly Poincar\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the construction and transformation properties of single-particle states, and the construction of GeV scale transition matrix elements. A simple model is utilized to demonstrate the feasibility of this approach.