Effective Action in Free Probability
Kurusch Ebrahimi-Fard, Frederic Patras
2024, v.30, Issue 1, 149-178
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.
doi:10.61102/1024-2953-mprf.2024.30.1.006
Keywords: effective action, free probability, free cumulants, planar Feynman diagrams, one-particle irreducibility
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