A variant of the S-matrix calculation of Epstein, Glaser and Scharf and its Hopf algebra structure

Alexander Lange

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Submission date: 28. Feb. 2000
Pages: 35
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Abstract:
Along the calculation of a perturbative S-matrix, created by Epstein and Glaser and further developed by Scharf, an algebra for the involved distributions is extracted. But its members turn out to be more singular than the distributions one has to split (causally) within the original procedure. Moreover, an antipode is introduced and the properties or a Hopf algebra are checked. That "rather unexpected" kind of formulating perturbative QFT, only recently discovered by Kreimer for the BPHZ-approach, is straightforwardly implemented. EGS' causality, implying locality, is substituted by time-reflection symmetry. The latter, being a consequence of EGS' assumption anyway, is motivated, here, starting with unitarity. The achieved Hopf algebra establishes the (combinatorial) connection to BPHZ's procedure, where time-reflections correspond to counterterms.