A Moyal-like product on functions is lifted to scalar fields and functionals, and its graph expansion is shown to reproduce the known adjacency-matrix description of Feynman graphs.
Quantum groups and quantum field theory: I. The free scalar field
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abstract
The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular structures can be built from the two-point function and the Feynman propagator of scalar fields to reproduce the operator product and the time-ordered product as twist deformations of the normal product. A correspondence is established between the quantum group and the quantum field concepts. On the mathematical side the underlying structures come out of Hopf algebra cohomology.
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From Kontsevich Graphs to Feynman graphs, a Viewpoint from the Star Products of Scalar Fields
A Moyal-like product on functions is lifted to scalar fields and functionals, and its graph expansion is shown to reproduce the known adjacency-matrix description of Feynman graphs.