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 TMF, 2000, Volume 123, Number 3, Pages 355–373 (Mi tmf609)

Test function space for Wick power series

A. G. Smirnov, M. A. Soloviev

P. N. Lebedev Physical Institute, Russian Academy of Sciences

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.

DOI: https://doi.org/10.4213/tmf609

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English version:
Theoretical and Mathematical Physics, 2000, 123:3, 709–725

Bibliographic databases:

Citation: A. G. Smirnov, M. A. Soloviev, “Test function space for Wick power series”, TMF, 123:3 (2000), 355–373; Theoret. and Math. Phys., 123:3 (2000), 709–725

Citation in format AMSBIB
\Bibitem{SmiSol00} \by A.~G.~Smirnov, M.~A.~Soloviev \paper Test function space for Wick power series \jour TMF \yr 2000 \vol 123 \issue 3 \pages 355--373 \mathnet{http://mi.mathnet.ru/tmf609} \crossref{https://doi.org/10.4213/tmf609} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794006} \zmath{https://zbmath.org/?q=an:1032.81531} \transl \jour Theoret. and Math. Phys. \yr 2000 \vol 123 \issue 3 \pages 709--725 \crossref{https://doi.org/10.1007/BF02551027} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000088926700001} 

• http://mi.mathnet.ru/eng/tmf609
• https://doi.org/10.4213/tmf609
• http://mi.mathnet.ru/eng/tmf/v123/i3/p355

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. G. Smirnov, M. A. Soloviev, “Spectral properties of Wick power series for a free field with an indefinite metric”, Theoret. and Math. Phys., 125:1 (2000), 1349–1362
2. A. G. Smirnov, M. A. Soloviev, “Wick Power Series Converging to Nonlocal Fields”, Theoret. and Math. Phys., 127:2 (2001), 632–645
3. M. A. Soloviev, “Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals”, Theoret. and Math. Phys., 128:3 (2001), 1252–1270
4. Smirnov, AG, “Towards Euclidean theory of infrared singular quantum fields”, Journal of Mathematical Physics, 44:5 (2003), 2058
5. S. S. Horuzhy, “Rigorous Formulation of a $2D$ Conformal Model in the Fock–Krein Space: Construction of the Global $\operatorname{Op}J^*$-Algebra of Fields and Currents”, Theoret. and Math. Phys., 141:1 (2004), 1381–1397
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