Scattering Theory for Quantum Fieldswith Indefinite Metric
Abstract
In this work, we discuss the scattering theory of local, relativistic quantum fields with indefinite metric. Since the results of HaagRuelle theory do not carry over to the case of indefinite metric [4], we propose an axiomatic framework for the construction of in and outstates, 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 outfields, 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/s002200000332
 arXiv:
 arXiv:mathph/0501031
 Bibcode:
 2001CMaPh.216..491A
 Keywords:

 Mathematical Physics;
 81T05;
 81T08
 EPrint:
 Commun.Math.Phys. 216 (2001) 491513