Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Menous, Frederic"'
We prove that the Catalan Lie idempotent $D_n(a,b)$, introduced in [Menous {\it et al.}, Adv. Appl. Math. 51 (2013), 177] can be refined by introducing $n$ independent parameters $a_0,\ldots,a_{n-1}$ and that the coefficient of each monomial is itsel
Externí odkaz:
http://arxiv.org/abs/2307.03001
We compute the expansion of the Catalan family of Lie idempotents introduced in [Menous et al., Adv. Applied Math. 51 (2013), 177-22] on the PBW basis of the Lie module. It is found that the coefficient of a tree depends only on its number of left an
Externí odkaz:
http://arxiv.org/abs/2005.08888
Publikováno v:
J. Math. Phys. 61, 092301 (2020)
We describe the resurgence properties of some partition functions corresponding to field theories in dimension 0. We show that these functions satisfy linear differential equations with polynomial coefficients and then use elementary stability result
Externí odkaz:
http://arxiv.org/abs/1910.01606
Autor:
Menous, Frédéric, Patras, Frédéric
In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with values in
Externí odkaz:
http://arxiv.org/abs/1703.07304
Publikováno v:
Advances in Applied Mathematics, Volume 88, July 2017, Pages 92-119
The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Fa\`a di Bruno algebra, and then to the group of a free operad over Schr\"oder trees. This leads to new combinatorial expressions, wh
Externí odkaz:
http://arxiv.org/abs/1604.04759
Autor:
Menous, Frédéric, Patras, Frédéric
Three equivalent methods allow to compute the antipode of the Hopf algebras of Feynman diagrams in perturbative quantum field theory (QFT): the Dyson-Salam formula, the Bogoliubov formula, and the Zimmermann forest formula. Whereas the first two hold
Externí odkaz:
http://arxiv.org/abs/1511.07403
We investigate the combinatorial properties of the functional equation $\phi[h(z)]=h(qz)$ for the conjugation of a formal diffeomorphism $\phi$ of $\mathbb{C}$ to its linear part $z\mapsto qz$. This is done by interpreting the functional equation in
Externí odkaz:
http://arxiv.org/abs/1506.08107
Autor:
Menous, Frederic
We study in this paper logarithmic derivatives associated to derivations on graded complete Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp-log correspondence between a Lie algebra
Externí odkaz:
http://arxiv.org/abs/1302.6037
Autor:
Fauvet, Frédéric, Menous, Frederic
We give a natural and complete description of Ecalle's mould-comould formalism within a Hopf-algebraic framework. The arborification transform thus appears as a factorization of characters, involving the shuffle or quasishuffle Hopf algebras, thanks
Externí odkaz:
http://arxiv.org/abs/1212.4740
Autor:
Menous, Frederic, Patras, Frédéric
Motivated by a recent surge of interest for Dynkin operators in mathematical physics and by problems in the combinatorial theory of dynamical systems, we propose here a systematic study of logarithmic derivatives in various contexts. In particular, w
Externí odkaz:
http://arxiv.org/abs/1206.4990