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TMF, 1971, Volume 9, Number 3, Pages 333–342 (Mi tmf4495)  

This article is cited in 3 scientific papers (total in 3 papers)

Conditions of consistency, completeness, and relativistic invariance of the algebra of equal-time commutators

Yu. M. Shirokov


Abstract: The problem of obtaining the necessary and sufficient conditions, which ensure the consistency, completeness and relativistic covariance of the system of equal-time commutators has been stated and solved.
The difficulties arise from the fact that the system of the commutators is cumbersome and put down in a noncovariant form. These difficulties have been tackled by the functorial transition from the category of quantum fields into the category of universal algebras. In the universal algebra each local quantity is represented by the corresponding element of the algebra. The elements of the algebra have no coordinate dependence. Each equal-time commutator is represented by the finite set of various nonassociative multiplications.
The energy stress tensor has to be included into the system of commutators for deriving the relativistic invariance conditions.

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English version:
Theoretical and Mathematical Physics, 1971, 9:3, 1176–1182

Bibliographic databases:

Received: 17.02.1971

Citation: Yu. M. Shirokov, “Conditions of consistency, completeness, and relativistic invariance of the algebra of equal-time commutators”, TMF, 9:3 (1971), 333–342; Theoret. and Math. Phys., 9:3 (1971), 1176–1182

Citation in format AMSBIB
\Bibitem{Shi71}
\by Yu.~M.~Shirokov
\paper Conditions of consistency, completeness, and relativistic invariance of the algebra of equal-time commutators
\jour TMF
\yr 1971
\vol 9
\issue 3
\pages 333--342
\mathnet{http://mi.mathnet.ru/tmf4495}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=471681}
\zmath{https://zbmath.org/?q=an:0243.70001}
\transl
\jour Theoret. and Math. Phys.
\yr 1971
\vol 9
\issue 3
\pages 1176--1182
\crossref{https://doi.org/10.1007/BF01043407}


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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. Yu. M. Shirokov, “Covariant formalism for equal-time commutators”, Theoret. and Math. Phys., 15:1 (1973), 329–344  mathnet  crossref  mathscinet
    2. Yu. M. Shirokov, “Canonical expansions of commutators and field products on the cone and at short distances in the universal algebra formalism”, Theoret. and Math. Phys., 25:1 (1975), 939–943  mathnet  crossref  mathscinet  zmath
    3. K. V. Indukaev, Yu. M. Shirokov, “Covariantization of the Boulware-Deser representation for the equal-time commutator of the energy-momentum tensor”, Theoret. and Math. Phys., 25:2 (1975), 1060–1064  mathnet  crossref  mathscinet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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