120 citations · 157 across the 4 of their papers we have counts for
8 papers · 1 filter
A Lie theoretic approach to renormalization
K. Ebrahimi-Fard, J. M. Gracia-Bondia, F. Patras
Motivated by recent work of Connes and Marcolli, based on the Connes-Kreimer approach to renormalization, we augment the latter by a combinatorial, Lie algebraic point of view. Our…
Hidden symmetry and Hopf algebra
Jose M. Gracia-Bondia
We spell two conundrums, one of physical and another of mathematical nature, and explain why one helps to elucidate the other
Combinatorics of renormalization as matrix calculus
K. Ebrahimi-Fard, J. M. Gracia-Bondia, L. Guo +1
We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calcula…
Position-dependent noncommutative products: classical construction and field theory
V. Gayral, J. M. Gracia-Bondia, F. Ruiz Ruiz
We look in Euclidean for associative star products realizing the commutation relation , where the noncommutativity parameters depend on the pos…
Trouble with space-like noncommutative field theory
V. Gayral, J. M. Gracia-Bondia, F. Ruiz Ruiz
It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already…
Combinatorial Hopf algebras in quantum field theory I
Hector Figueroa, Jose M. Gracia-Bondia
This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as…