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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 143, Number 2, Pages 195–210
DOI: https://doi.org/10.4213/tmf1810
(Mi tmf1810)
 

This article is cited in 2 scientific papers (total in 2 papers)

Two classes of generalized functions used in nonlocal field theory

M. A. Soloviev

P. N. Lebedev Physical Institute, Russian Academy of Sciences
Full-text PDF (304 kB) Citations (2)
References:
Abstract: We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space $S^0$ (which is the Fourier transform of the Schwartz space $\mathcal D$) and using test functions in the Gelfand–Shilov spaces $S^0_\alpha$. We prove that every functional defined on $S^0$ has the same carrier cones as its restrictions to the smaller spaces $S^0_\alpha$. As an application of this result, we derive a Paley–Wiener–Schwartz-type theorem for arbitrarily singular generalized functions of tempered growth and obtain the corresponding extension of Vladimirovs algebra of functions holomorphic in a tubular domain.
Keywords: nonlocal quantum fields, causality, Wightman functions, analytic functionals, Hörmanders estimates, Paley–Wiener–Schwartz-type theorems.
Received: 02.07.2004
English version:
Theoretical and Mathematical Physics, 2005, Volume 143, Issue 2, Pages 651–663
DOI: https://doi.org/10.1007/s11232-005-0096-8
Bibliographic databases:
Language: Russian
Citation: M. A. Soloviev, “Two classes of generalized functions used in nonlocal field theory”, TMF, 143:2 (2005), 195–210; Theoret. and Math. Phys., 143:2 (2005), 651–663
Citation in format AMSBIB
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\paper Two classes of generalized functions used in nonlocal field theory
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  • https://www.mathnet.ru/eng/tmf/v143/i2/p195
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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