Unstable particles in non-relativistic quantum mechanics?

TL;DR

This paper argues that the traditional non-relativistic quantum mechanics framework neglects certain physical effects related to phase invariance, and proposes an extended group approach to better describe unstable particles.

Contribution

It introduces the Extended Galilei group to incorporate phase effects, challenging Bargmann's superselection rule and enabling a consistent non-relativistic description of unstable particles.

Findings

Bargmann's superselection rule neglects physical effects.

Extended Galilei group accounts for phase effects.

Allows consistent non-relativistic description of unstable particles.

Abstract

The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of states with different masses and implies that unstable particles cannot be described consistently in non-relativistic quantum mechanics. In this paper we claim that Bargmann's rule neglects physical effects and that a proper description of non-relativistic quantum mechanics requires to take into account this phase through the Extended Galilei group and the definition of its action on spacetime coordinates.