Abstract:
Applications of the theory of elliptic operators in quantum field theory are indicated. The concept of the statistical sum of a degenerate elliptic functional is introduced; this concept finds application both in quantum field theory and outside it (for the construction of invariants of the type of the Ray–Singer torsion).
Citation:
A. S. Schwarz, “Elliptic operators in quantum field theory”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 17, VINITI, Moscow, 1981, 113–173; J. Soviet Math., 21:4 (1983), 551–601
\Bibitem{Sch81}
\by A.~S.~Schwarz
\paper Elliptic operators in quantum field theory
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat.
\yr 1981
\vol 17
\pages 113--173
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd49}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=628977}
\zmath{https://zbmath.org/?q=an:0509.35071|0482.35080}
\transl
\jour J. Soviet Math.
\yr 1983
\vol 21
\issue 4
\pages 551--601
\crossref{https://doi.org/10.1007/BF01084286}
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https://www.mathnet.ru/eng/intd49
https://www.mathnet.ru/eng/intd/v17/p113
This publication is cited in the following 6 articles:
L. A. Takhtajan, “Etudes of the resolvent”, Russian Math. Surveys, 75:1 (2020), 147–186
D. Wallenta, “Elliptic Quasicomplexes on Compact Closed Manifolds”, Integr. Equ. Oper. Theory, 73:4 (2012), 517
M. Hazewinkel, Encyclopaedia of Mathematics, 1993, 513
P. G. Zograf, L. A. Takhtadzhyan, “On the geometry of moduli spaces of vector bundles over a Riemann surface”, Math. USSR-Izv., 35:1 (1990), 83–100
P. G. Zograf, L. A. Takhtadzhyan, “A local index theorem for families of $\bar \partial$-operators on Riemann surfaces”, Russian Math. Surveys, 42:6 (1987), 169–190
Yu. N. Kafiev, “One-loop corrections in the O(5) Skyrme model”, Theoret. and Math. Phys., 61:2 (1984), 1133–1144
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