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On the product of distributions with coincident point singularities. (English) Zbl 0966.81047

Summary: We generalize the result obtained by A. González Domínguez and R. Scarfiello [Rev. Un. Mat. Argentina, Volumen de Homenaje a Beppo Levi, 53-67 (1956; Zbl 0072.31902)]; and B. Fisher, Proc. Camb. Philos. Soc. 72, 201-204 (1972; Zbl 0239.46031)]. This result can be used in quantum field theory for the evaluation of products of propagators of the fields. With this new result we obtain the product \((c^2+ P)^{-n}\cdot\delta^{m- 1}(c^2+ p)\). As a physical example, we evaluate the self-energy Green function of a massless scalar field.

MSC:

81T15 Perturbative methods of renormalization applied to problems in quantum field theory
46F99 Distributions, generalized functions, distribution spaces
81T99 Quantum field theory; related classical field theories
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