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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 128, Number 3, Pages 492–514
DOI: https://doi.org/10.4213/tmf511
(Mi tmf511)
 

This article is cited in 8 scientific papers (total in 8 papers)

Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals

M. A. Soloviev

P. N. Lebedev Physical Institute, Russian Academy of Sciences
Full-text PDF (371 kB) Citations (8)
References:
Abstract: We generalize the theory of Lorentz-covariant distributions to broader classes of functionals including ultradistributions, hyperfunctions, and analytic functionals with a tempered growth. We prove that Lorentz-covariant functionals with essential singularities can be decomposed into polynomial covariants and establish the possibility of the invariant decomposition of their carrier cones. We describe the properties of odd highly singular generalized functions. These results are used to investigate the vacuum expectation values of nonlocal quantum fields with an arbitrary high-energy behavior and to extend the spin-statistics theorem to nonlocal field theory.
Received: 15.05.2001
English version:
Theoretical and Mathematical Physics, 2001, Volume 128, Issue 3, Pages 1252–1270
DOI: https://doi.org/10.1023/A:1012368004774
Bibliographic databases:
Language: Russian
Citation: M. A. Soloviev, “Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals”, TMF, 128:3 (2001), 492–514; Theoret. and Math. Phys., 128:3 (2001), 1252–1270
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf511
  • https://doi.org/10.4213/tmf511
  • https://www.mathnet.ru/eng/tmf/v128/i3/p492
  • This publication is cited in the following 8 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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    Abstract page:363
    Full-text PDF :187
    References:38
    First page:1
     
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