A short essay on the interplay between algebraic language theory, galois theory and class field theory : comparing physics and theory of computation (Mathematical aspects of quantum fields and related topics)

Abstract

This paper is written as a technical report for our talk given at the RJMS workshop on quantum fields and related topics, held on 6th- 8th December 2021. In this talk we introduced our recent works [23, 24, 25, 26] in formal language theory to the community of mathematical physics, which concern some interplay between algebraic language theory, galois theory and class field theory. In this paper we discuss some conceptual contents of our recent works [23, 24, 25, 26] in more detail.