Scattering theory for quantum fields with indefinite metric

Details Scattering theory for quantum fields with indefinite metric Scattering theory for quantum fields with indefinite metric

2005-01-12

arxiv.org/abs/math-ph/0501031v1

Commun.Math.Phys. 216 (2001) 491-513

Physics

Mathematical Physics

Scientific paper

10.1007/s002200000332

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.

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