Test Function Space for Wick Power Series

Details Test Function Space for Wick Power Series Test Function Space for Wick Power Series

2000-10-02

arxiv.org/abs/math-ph/0010001v3

Theor. Math. Phys. 123 (2000) 709-725

Physics

Mathematical Physics

24 pages LaTeX; typos corrected

Scientific paper

10.1007/BF02551027

We derive a criterion that is convenient for applications and exactly characterizes the test function space on 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 on the systematic use of the analytic properties of the Hilbert majorant of the indefinite metric and on the application of a suitable theorem on the unconditional convergence of series of boundary values of analytic functions.

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