Effective Action in Free Probability
Mathematical Physics
2024-09-24 v1 Combinatorics
math.MP
Probability
Rings and Algebras
Abstract
Recent works have explored relations between classical and quantum statistical physics on the one hand and Voiculescu's theory of free probability on the other. Motivated by these results, the present work focuses on the notion of effective action, which is closely related to the large deviation rate function in classical probability and one-particle irreducible correlation functions in quantum field theories. The central aim is to understand how it can be defined and studied in free probability. In this respect, we introduce a suitable diagrammatic formalism.
Cite
@article{arxiv.2305.08871,
title = {Effective Action in Free Probability},
author = {Kurusch Ebrahimi-Fard and Frederic Patras},
journal= {arXiv preprint arXiv:2305.08871},
year = {2024}
}