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Power series of the free field as operator-valued functional on spaces of typeS

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Abstract

Infinite series of Wick powers of the free, massive Bose field are analysed in terms of test function spaces of typeS for arbitrary space dimension. By direct estimates of the smeared phase space integrals sufficiency conditions for the existence of the vacuum expectation values are derived. These conditions are shown to be precise. The field-operators are defined on a dense invariant domain in Fock space, where they satisfy the Wightman axioms with the possible exception of locality. Localisable and nonlocalisable fields are dealt within the same frame. The behaviour of spectral functions and the strength of singularities are discussed.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Tübingen, Germany

    A. Rieckers

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  1. A. Rieckers
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This work was supported by the Deutsche Forschungsgemeinschaft.

This work is part of a thesis submitted to the Naturwissenschaftlichen Fakultät der Universität München.

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Rieckers, A. Power series of the free field as operator-valued functional on spaces of typeS . Int J Theor Phys 4, 55–82 (1971). https://doi.org/10.1007/BF00671382

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  • DOI: https://doi.org/10.1007/BF00671382

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