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

Abstract

We prove that for a Wightman quantum field $\varphi (x)$ the assumptions (i) positivity of the metric on the state space $\mathcal{H}$ 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.

References in corpus (3)

• Models of local relativistic quantum fields with indefinite metric (in all dimensions)
• Scattering theory for quantum fields with indefinite metric
• A Characterisation of Locality in Momentum Space

Cited by in corpus (2)

• Nontrivial models with indefinite metric
• Quantum fields obtained from convoluted generalized white noise never have positive metric