Applications of Lévy Differential Operators in the Theory of Gauge Fields

被引：0
|
作者：
Volkov B.O. [1 ,2 ]
机构：
[1] V. A. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow
[2] Bauman Moscow State Technical University, Moscow
来源：
Journal of Mathematical Sciences | 2021年 / 252卷 / 1期
关键词：
60H40; 81T13; gauge field; instanton; Lévy divergence; Lévy Laplacian; Malliavin calculus; Yang–Mills equations;
D O I：
10.1007/s10958-020-05138-9
中图分类号：
学科分类号：
摘要：
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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
引用
收藏
页码：20 / 35
页数：15
相关论文
共 50 条
  • [1] On Properties and Applications of Gaussian Subordinated Lévy Fields
    Robin Merkle
    Andrea Barth
    Methodology and Computing in Applied Probability, 2023, 25
  • [2] Levy differential operators and Gauge invariant equations for Dirac and Higgs fields
    Volkov, Boris O.
    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2019, 22 (01)
  • [3] Multifractal analysis of Lévy fields
    Arnaud Durand
    Stéphane Jaffard
    Probability Theory and Related Fields, 2012, 153 : 45 - 96
  • [4] Multifractal analysis of L,vy fields
    Durand, Arnaud
    Jaffard, Stephane
    PROBABILITY THEORY AND RELATED FIELDS, 2012, 153 (1-2) : 45 - 96
  • [5] Liouville's theorems for Lévy operators
    Grzywny, Tomasz
    Kwasnicki, Mateusz
    MATHEMATISCHE ANNALEN, 2024,
  • [6] LP Theory of Differential Forms and Related Operators with Applications
    Ding, Shusen
    Wang, Yong
    Shi, Peilin
    Xing, Yuming
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [7] INFINITESIMAL GAUGE OPERATORS FOR PSEUDOSCALAR FIELDS
    井思聪
    阮图南
    范洪义
    ActaMathematicaScientia, 1995, (02) : 121 - 125
  • [8] INFINITESIMAL GAUGE OPERATORS FOR PSEUDOSCALAR FIELDS
    JING, SC
    RAUN, TN
    FAN, HY
    ACTA MATHEMATICA SCIENTIA, 1995, 15 (02) : 121 - 125
  • [9] Surface operators in gauge theory
    Witten, Edward
    FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 2007, 55 (5-7): : 545 - 550
  • [10] Representations of homogeneous quantum Lévy fields
    V. P. Belavkin
    L. Gregory
    Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2006, 116 : 477 - 488
12345