Variational Dual Solutions of Chern-Simons Theory

2024/11/26 by Amit Acharya, Acharya, Amit, Janusz Ginster +3 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quantum many-body systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2411.17635

openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A scheme for generating weakly lower semi-continuous action functionals corresponding to the Euler-Lagrange equations of Chern-Simons theory is described. Coercivity is deduced for such a functional in appropriate function spaces to prove the existence of a minimizer, which constitutes a solution to the Euler-Lagrange equations of Chern-Simons theory in a relaxed sense. A geometric analysis is also made, especially for the gauge group SU(2), relating connection forms on the bundle to corresponding forms in the dual scheme.

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