A three-parameter Hopf deformation of the algebra of Feynman-like diagrams

Duchamp, G. H. E.; Blasiak, P.; Horzela, A.; Penson, K. A. and Solomon, A. I. (2010). A three-parameter Hopf deformation of the algebra of Feynman-like diagrams. Journal of Russian Laser Research, 31(2) pp. 162–181.

DOI: https://doi.org/10.1007/s10946-010-9135-5

Abstract

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 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 (MQSym) 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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