Scattering theory for quantum fields with indefinite metric

TL;DR

This paper develops a new axiomatic framework for scattering theory in quantum fields with indefinite metric, overcoming limitations of Haag--Ruelle theory and enabling the construction of in- and out- states.

Contribution

It introduces the form factor functional and a Hilbert space structure condition to extend scattering theory to indefinite metric quantum fields.

Findings

Constructed local, relativistic quantum fields with indefinite metric from polynomial scattering matrices.

Derived LSZ asymptotic condition within the new axiomatic framework.

Established a method to build in- and out- states for indefinite metric quantum fields.

Abstract

In this work, we discuss the scattering theory of local, relativistic quantum fields with indefinite metric. Since the results of Haag--Ruelle theory do not carry over to the case of indefinite metric, we propose an axiomatic framework for the construction of in- and out- states, such that the LSZ asymptotic condition can be derived from the assumptions. The central mathematical object for this construction is the collection of mixed vacuum expectation values of local, in- and out- fields, called the ``form factor functional'', which is required to fulfill a Hilbert space structure condition. Given a scattering matrix with polynomial transfer functions, we then construct interpolating, local, relativistic quantum fields with indefinite metric, which fit into the given scattering framework.