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On the Renormalization of Feynman Integrals
Author(s) -
Westwater M. J.
Publication year - 1969
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19690170102
Subject(s) - feynman diagram , renormalization , feynman integral , path integral formulation , volume integral , mathematics , functional integration , mathematical physics , multiple integral , regularization (linguistics) , euclidean geometry , gaussian integral , improper integral , physics , mathematical analysis , integral equation , quantum mechanics , fourier integral operator , geometry , artificial intelligence , computer science , quantum
An arbitrary Feynman integral is considered for external momenta in the Euclidean region, the usual rotation of energy contours having been used to write the integral as an integral over Euclidean internal momenta. A compactification of the space of internal momenta is defined, and the Feynman integral is written as the integral of a current on this compact manifold. This presentation of the integral is used to give a proof of the convergence criterion for Feynman integrals, and to show that a well‐defined renormalized integral may be obtained by a subtraction operation or by analytic renormalization.