Andreas U. Schmidt
Infinite Infrared Regularization and a State Space for the Heisenberg Algebra
(72K, AMS-TeX)
ABSTRACT. 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.