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

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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 ϑ 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.

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Authors and Affiliations

  1. Institute for Nuclear Research, RAS, Moscow, Russia

    Yu. S. Vernov

  2. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia

    M. N. Mnatsakanova

Authors
  1. Yu. S. Vernov
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  2. M. N. Mnatsakanova
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 388–403, February, 2005.

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Vernov, Y.S., Mnatsakanova, M.N. Jost-Lehmann-Dyson representation, analyticity in the angular variable, and upper bounds in noncommutative quantum field theory. Theor Math Phys 142, 324–336 (2005). https://doi.org/10.1007/s11232-005-0015-z

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  • DOI: https://doi.org/10.1007/s11232-005-0015-z

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