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We construct a three parameter deformation of the Hopf algebra $mathbf{LDIAG}$. This new algebra is a true Hopf deformation which reduces to $mathbf{LDIAG}$ on one hand and to $mathbf{MQSym}$ on the other, relating $mathbf{LDIAG}$ to other Hopf algebras of interest in contemporary physics. Further, its product law reproduces that of the algebra of polyzeta functions.
We construct a three-parameter deformation of the Hopf algebra $LDIAG$. This is the algebra that appears in an expansion in terms of Feynman-like diagrams of the {em product formula} in a simplified version of Quantum Field Theory. This new algebra i
This paper together with the previous one (arXiv:hep-th/0604146) presents the detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf algebra in terms of complex and real generators. We describe here in detail two quantum defo
We look at a graph property called reducibility which is closely related to a condition developed by Brown to evaluate Feynman integrals. We show for graphs with a fixed number of external momenta, that reducibility with respect to both Symanzik poly
We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra indu
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based on based