Nontrivial models of quantum fields with indefinite metric

The non perturbative construction of quantum field models with nontrivial scattering in arbitrary dimension d of the underlying Minkowski space-time is much more simple in the framework of quantum field theory with indefinite metric than in the positive metric case. In particular, there exist a number of solutions in the physical dimension d = 4, where up to now no positive metric solutions are known. Here we review, why this is so, and we discuss some examples obtained by analytic continuation from the solutions of Euclidean covariant stochastic partial differential equations (SPDEs) driven by non-Gaussian white noise.

[1]  S. Albeverio,et al.  Representing Euclidean Quantum Fields as Scaling Limit of Particle Systems , 2002, math-ph/0501029.

[2]  H. Gottschalk.  On the stability of one-particle states generated by quantum fields fulfilling Yang—Feldman equations , 2001, math-ph/0408050.

[3]  S. Albeverio,et al.  Scattering Theory for Quantum Fields¶with Indefinite Metric , 2001, math-ph/0501031.

[4]  N. Nikolov,et al.  Rationality of Conformally Invariant Local Correlation Functions on Compactified Minkowski Space , 2000, hep-th/0009004.

[5]  Perturbative Quantum Electrodynamics and Axiomatic Field Theory , 2000, Texts and Monographs in Physics.

[6]  L. Streit,et al.  Construction of relativistic quantum fields in the framework of white noise analysis , 1999 .

[7]  S. Albeverio,et al.  Models of Local Relativistic Quantum Fields with Indefinite Metric (in All Dimensions) , 1997, math-ph/0409057.

[8]  S. Albeverio,et al.  CONVOLUTED GENERALIZED WHITE NOISE, SCHWINGER FUNCTIONS AND THEIR ANALYTIC CONTINUATION TO WIGHTMAN FUNCTIONS , 1996 .

[9]  R. Gielerak,et al.  Covariant SPDEs and quantum field structures , 1996, funct-an/9607001.

[10]  F. Strocchi.  Selected Topics on the General Properties of Quantum Field Theory: Lecture Notes , 1993 .

[11]  Infrared singularities, vacuum structure and pure phases in local quantum field theory , 1980 .

[12]  Christian Berg,et al.  Potential Theory on Locally Compact Abelian Groups , 1975 .

[13]  On the algebra of test functions for field operators , 1973 .

[14]  Robert Schrader,et al.  Axioms for Euclidean Green's functions II , 1973 .

[15]  A. Wightman,et al.  PCT, spin and statistics, and all that , 1964 .

[16]  Suraj N. Gupta.  Theory of longitudinal photons in quantum electrodynamics , 1950 .