A Three Parameter Hopf Deformation of the Algebra of Feynman-like Diagrams

Details A Three Parameter Hopf Deformation of the Algebra of Feynman-like Diagrams A Three Parameter Hopf Deformation of the Algebra of Feynman-like Diagrams

2007-04-19

arxiv.org/abs/0704.2522v2

Physics

Mathematical Physics

Scientific paper

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 is a true Hopf deformation which reduces to $\LDIAG$ for some parameter values and to the algebra of Matrix Quasi-Symmetric Functions ($\MQS$) for others, and thus relates $\LDIAG$ to other Hopf algebras of contemporary physics. Moreover, there is an onto linear mapping preserving products from our algebra to the algebra of Euler-Zagier sums.

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