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
  • [41] COHOMOLOGY THEORY OF DIFFERENTIAL OPERATORS
    王继春
    ActaMathematicaScientia, 1990, (01) : 79 - 84
  • [42] SEPARABLE DIFFERENTIAL OPERATORS AND APPLICATIONS
    Shakhmurov, Veli B.
    MOSCOW MATHEMATICAL JOURNAL, 2016, 16 (02) : 299 - 321
  • [43] Lévy--Laplace Operators in Functional Rigged Hilbert Spaces
    L. Accardi
    O. G. Smolyanov
    Mathematical Notes, 2002, 72 : 129 - 134
  • [44] Option Pricing for Symmetric Lévy Returns with Applications
    Hamza K.
    Klebaner F.C.
    Landsman Z.
    Tan Y.-O.
    Asia-Pacific Financial Markets, 2015, 22 (1) : 27 - 52
  • [45] Interior Schauder Estimates for Elliptic Equations Associated with Lévy Operators
    Franziska Kühn
    Potential Analysis, 2022, 56 : 459 - 481
  • [46] Stability of complement value problems for p-Lévy operators
    Foghem, Guy
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2025, 32 (01):
  • [47] On the Boundary Theory of Subordinate Killed Lévy Processes
    Panki Kim
    Renming Song
    Zoran Vondraček
    Potential Analysis, 2020, 53 : 131 - 181
  • [48] Nonlinear Operators in Fixed Point Theory with Applications to Fractional Differential and Integral Equations
    Ahmad, Jamshaid
    Al-Rawashdeh, Ahmad Saleh
    Nazir, Talat
    Parvaneh, Vahid
    De la Sen, Manuel
    JOURNAL OF FUNCTION SPACES, 2018, 2018
  • [49] THEORY OF GRADUATED DIFFERENTIAL OPERATORS ON DIFFERENTIAL FORMS
    BUTTIN, C
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1974, 102 (01): : 49 - 73
  • [50] Exact joint laws associated with spectrally negative L,vy processes and applications to insurance risk theory
    Yin, Chuancun
    Yuen, Kam C.
    FRONTIERS OF MATHEMATICS IN CHINA, 2014, 9 (06) : 1453 - 1471
12345