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arXiv · 1210.5448

On-shell extension of distributions

Dorothea Bahns·Michał Wrochna
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Abstract

We consider distributions on $\R^n\setminus{0}$ which satisfy a given set of partial differential equations and provide criteria for the existence of extensions to $\R^n$ that satisfy the same set of equations on $\R^n$. We use the results to construct distributions satisfying specific renormalisation conditions in the Epstein and Glaser approach to perturbative quantum field theory. Contrary to other approaches, we provide a unified apporach to treat Lorentz covariance, invariance under global gauge group and almost homogeneity, as well as discrete symmetries. We show that all such symmetries can be recovered by applying a linear map defined for all degrees of divergence. Using similar techniques, we find a relation between on-shell and off-shell time-ordered products involving higher derivatives of the fields.

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Dorothea Bahns, Michał Wrochna. 2014-05-05. On-shell extension of distributions. https://doi.org/10.1007/s00023-013-0288-y

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