On the stability of one particle states generated by quantum fields fulfilling Yang-Feldman equations

TL;DR

This paper proves that under certain conditions, states generated by quantum fields satisfying Yang-Feldman equations are stable in a positive metric space, but not in indefinite metric spaces, highlighting the importance of metric positivity.

Contribution

It establishes a stability result for one-particle states generated by quantum fields fulfilling Yang-Feldman equations within positive metric frameworks.

Findings

States are stable in positive metric spaces under specified conditions.

Counterexample shows instability in indefinite metric quantum fields.

Highlights the role of metric positivity in quantum field stability.

Abstract

We prove that for a Wightman quantum field $\phi(x)$ the assumptions (i) positivity of the metric on the state space ${\cal H}$ of the theory (ii) the asymptotic condition in the form of Yang-Feldman equations and (iii) Klein-Gordon equation for the outgoing field imply that the states generated by application of the asymptotic fields to the vacuum are stable. We prove by a counter example that this statement is wrong in the case of quantum fields with indefinite metric.