TY - JOUR
A1 - Schmidt, Andreas U.
T1 - Infinite infrared regularization and a state space for the Heisenberg algebra
N2 - We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand-Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity. See the corresponding paper: Schmidt, Andreas U.: "Mathematical Problems of Gauge Quantum Field Theory: A Survey of the Schwinger Model" and the presentation "Infinite Infrared Regularization in Krein Spaces"
KW - Infrared singularity
KW - Gelfand-Shilov space
KW - Heisenberg algebra
KW - indefinite inner product space
KW - Krein space
Y1 - 2003
UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4353
UR - https://nbn-resolving.org/urn:nbn:de:hebis:30-11331
SN - 0022-2488
SN - 1089-7658
N1 - Aktualisierte Fassung, zuerst erschienen in: Journal of mathematical physics, 43.2002, Nr. 1, S. 243-259, Erratum erschienen in: Journal of mathematical physics, 43.2002, Nr. 6, S. 3412
SP - 1
EP - 18
ER -