120 citations · 691 across the 56 of their papers we have counts for
10 papers · 1 filter
Effective Action in Free Probability
Kurusch Ebrahimi-Fard, Frederic Patras
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…
Algebraic structures underlying quantum independences : Theory and Applications
Raphael Chetrite, Frederic Patras
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebr…
The combinatorics of Green's functions in planar field theories
Kurusch Ebrahimi-Fard, Frederic Patras
The aim of this work is to outline in some detail the use of combinatorial algebra in planar quantum field theory. Particular emphasis is given to the relations between the differe…
A Fast Algorithm for the Construction of Integrity Bases Associated to Symmetry-Adapted Polynomial Representations. Application to Tetrahedral XY4 Molecules
Patrick Cassam-Chenaï, Guillaume Dhont, Frédéric Patras
Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the constr…
Time-ordering and a generalized Magnus expansion
Michel Bauer, Raphael Chetrite, Kurusch Ebrahimi-Fard +1
Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering an…
Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes
Kurusch Ebrahimi-Fard, Frederic Patras
This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a m…
Nonlocal, noncommutative diagrammatics and the linked cluster Theorems
Christian Brouder, Patras Frédéric
Recent developments in quantum chemistry, perturbative quantum field theory, statistical physics or stochastic differential equations require the introduction of new families of Fe…
Exponential renormalization
Kurusch Ebrahimi-Fard, Frederic Patras
Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's function…
Hyperoctahedral Chen calculus for effective Hamiltonians
Christian Brouder, Frédéric Patras
The algebraic structure of iterated integrals has been encoded by Chen. Formally, it identifies with the shuffle and Lie calculus of Lyndon, Ree and Schützenberger. It is mostly in…
A Zassenhaus-type algorithm solves the Bogoliubov recursion
Kurusch Ebrahimi-Fard, Frederic Patras
This paper introduces a new Lie-theoretic approach to the computation of counterterms in perturbative renormalization. Contrary to the usual approach, the devised version of the Bo…