Work

Correlation Functions Involving Dirac Fields from Homotopy Algebras I: The Free Theory

Year: 2025

Type: article

Abstract: We extend the formula for correlation functions of scalar field theories in terms of quantum $A_\infty$ algebras, presented in arXiv:2203.05366, to incorporate Dirac fields. We use a description that is analogous to string field theory, and the formula for correlation functions takes the same form for both scalar fields and Dirac fields. We prove that correlation functions from our formula satisfy the Schwinger–Dyson equations in the free theory. The proof for interacting theories is presented in the companion paper arXiv:2305.13103 by one of the authors. We also explain the relation of our formula to the definition of correlation functions in the approach by Costello and Gwilliam based on factorization algebras.

Source: Progress of Theoretical and Experimental Physics

DOI: 10.1093/ptep/ptaf027

Authors: Keisuke Konosu, Yuji Okawa

Institution: The University of Tokyo

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $979

Funder: Japan Society for the Promotion of Science