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Test function space for Wick power series

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Abstract

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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Authors and Affiliations

  1. Lebedev Physical Institute, RAS, Moscow, Russia

    A. G. Smirnov & M. A. Solov'ev

Authors
  1. A. G. Smirnov
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  2. M. A. Solov'ev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 355–373, June, 2000.

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Smirnov, A.G., Solov'ev, M.A. Test function space for Wick power series. Theor Math Phys 123, 709–725 (2000). https://doi.org/10.1007/BF02551027

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  • DOI: https://doi.org/10.1007/BF02551027

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