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Test function space for Wick power series. (English. Russian original) Zbl 1032.81531

Theor. Math. Phys. 123, No. 3, 709-725 (2000); translation from Teor. Mat. Fiz. 123, No. 3, 355-373 (2000).
Summary: We derive a criterion that is convenient for applications and exactly characterizes the test function space an which the operator realization of a given series of Wick powers of a free field is possible. The suggested derivation does not use the assumption that the metric of the state space is positive and can therefore be used in a gauge theory. It is based an the systematic use of the analytic properties of the Hilbert majorant of the indefinite metric and an the application of a suitable theorem an the unconditional convergence of series of boundary values of analytic functions.

MSC:

81T05 Axiomatic quantum field theory; operator algebras
46N50 Applications of functional analysis in quantum physics
46F05 Topological linear spaces of test functions, distributions and ultradistributions
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References:

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