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A multipurpose Hopf deformation of the Algebra of Feynman-like Diagrams

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 نشر من قبل Gerard Henry Edmond Duchamp
 تاريخ النشر 2006
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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.



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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 s 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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