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TMF, 2005, Volume 142, Number 2, Pages 388–402 (Mi tmf1790)  

This article is cited in 1 scientific paper (total in 1 paper)

Jost–Lehmann–Dyson representation, analyticity in the angular variable, and upper bounds in noncommutative quantum field theory

Yu. S. Vernova, M. N. Mnatsakanovab

a Institute for Nuclear Research, Russian Academy of Sciences
b Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: We prove the existence of an analogue of the Jost–Lehmann–Dyson representation in noncommutative quantum field theory for the case where the noncommutativity affects only the spatial variables. Using this representation, we show that there is a certain class of elastic scattering amplitudes that have an analytic continuation to the complex $\cos\vartheta$ plane with the Martin ellipse as the related analyticity domain. Using the analyticity in the angular variable and the unitarity as a basis, we establish an analogue of the Froissart–Martin bound for the total cross section in the noncommutative case.

Keywords: noncommutativity, quantum field theory, local commutativity, analyticity, unitarity, Jost–Lehmann–Dyson representation, Lehmann ellipse, Martin ellipse, Froissart–Martin bound

DOI: https://doi.org/10.4213/tmf1790

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English version:
Theoretical and Mathematical Physics, 2005, 142:2, 324–336

Bibliographic databases:


Citation: Yu. S. Vernov, M. N. Mnatsakanova, “Jost–Lehmann–Dyson representation, analyticity in the angular variable, and upper bounds in noncommutative quantum field theory”, TMF, 142:2 (2005), 388–402; Theoret. and Math. Phys., 142:2 (2005), 324–336

Citation in format AMSBIB
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\by Yu.~S.~Vernov, M.~N.~Mnatsakanova
\paper Jost--Lehmann--Dyson representation, analyticity in the angular variable, and upper bounds in noncommutative quantum field theory
\jour TMF
\yr 2005
\vol 142
\issue 2
\pages 388--402
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\crossref{https://doi.org/10.4213/tmf1790}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2141786}
\zmath{https://zbmath.org/?q=an:1178.81263}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2005TMP...142..324V}
\elib{http://elibrary.ru/item.asp?id=9135956}
\transl
\jour Theoret. and Math. Phys.
\yr 2005
\vol 142
\issue 2
\pages 324--336
\crossref{https://doi.org/10.1007/s11232-005-0015-z}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000227756500015}


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  • https://doi.org/10.4213/tmf1790
  • http://mi.mathnet.ru/eng/tmf/v142/i2/p388

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. S. Vernov, M. N. Mnatsakanova, “Wightman axiomatic approach in noncommutative field theory”, Theoret. and Math. Phys., 142:2 (2005), 337–348  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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