Applications of Lévy differential operators in the theory of gauge fields. (English. Russian original) Zbl 1468.60087
J. Math. Sci., New York 252, No. 1, 20-35 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 151, 21-36 (2018).
Summary: This paper is a survey of results on the relationship between gauge fields and infinitedimensional equations for parallel transport that contain the Lévy Laplacian or the divergence associated with this Laplacian. Also we analyze the deterministic case where parallel transports are operator-valued functionals on the space of curves and the case of the Malliavin calculus where (stochastic) parallel transports are operator-valued Wiener functionals.
MSC:
| 60H40 | White noise theory |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 81S25 | Quantum stochastic calculus |
Keywords:
Lévy Laplacian; Lévy divergence; gauge field; Yang-Mills equations; instanton; Malliavin calculusReferences:
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