TL;DR
This paper explores the connections between heat kernel measures on infinite-dimensional Lie groups, critical Sobolev limits, and Feynman-Kac measures in sigma models, highlighting their interrelations in mathematical physics.
Contribution
It provides an exposition linking heat kernels, Sobolev critical limits, and Feynman-Kac measures, clarifying their relationships in infinite-dimensional analysis.
Findings
Established connections between heat kernels and Sobolev critical limits.
Analyzed Feynman-Kac measures in the context of sigma models.
Provided insights into infinite-dimensional Lie group measures.
Abstract
This paper is an exposition of several questions linking heat kernel measures on infinite dimensional Lie groups, limits associated with critical Sobolev exponents, and Feynmann-Kac measures for sigma models.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometry and complex manifolds · Advanced Mathematical Modeling in Engineering