7 citations · 25 across the 6 of their papers we have counts for
10 papers
On deformation theory and graph homology
Fusun Akman, Lucian M. Ionescu, Papa A. Sissokho
Deformation theory of associative algebras and in particular of Poisson algebras is reviewed. The role of an almost contraction leading to a canonical solution of the corresponding…
A canonical semi-classical star-product
Lucian M. Ionescu, Papa A. Sissokho
We study the Maurer-Cartan equation of the pre-Lie algebra of graphs controling the deformation theory of associative algebras and prove that there is a canonical solution within t…
Cohomology of Feynman graphs and perturbative quantum field theory
Lucian M. Ionescu
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. Th…
A combinatorial approach to coefficients in deformation quantization
Lucian M. Ionescu
Graph cocycles for star-products are investigated from the combinatorial point of view, using Connes-Kreimer renormalization techniques. The Hochschild complex, controlling the def…
A Hopf algebra deformation approach to renormalization
Lucian M. Ionescu, Michael Marsalli
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence b…
Perturbative Quantum Field Theory and Configuration Space Integrals
Lucian M. Ionescu
L-infinity morphisms are studied from the point of view of perturbative quantum field theory, as generalizations of Feynman expansions. The connection with the Hopf algebra approac…