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Feynman Amplitudes as Tempered Distributions
Author(s) -
Smirnov V. A.
Publication year - 1985
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190330902
Subject(s) - meromorphic function , feynman diagram , renormalization , representation (politics) , mathematical physics , amplitude , operator (biology) , physics , convergence (economics) , mathematics , mathematical analysis , quantum mechanics , biochemistry , chemistry , repressor , politics , political science , transcription factor , law , economics , gene , economic growth
Feynman amplitudes (FA) are analyzed with the help of the method which employs as much as possible the analogy between ultraviolet (UV) and infrared (IR) divergences and is based on a modified α‐representation. It is proved that an analytically and/or dimensionally regularized FA is a tempered distribution of external momenta and a meromorphic function of regularizing parameters with UV and IR poles. An absolutely convergent α‐representation of analytically and/or dimensionally regularized FA is derived in various analyticity domains. This representation is obtained from the α‐representation in the initial domain of convergence by inserting the operator which has the same structure as the R *‐operation that is a generalization of the dimensional renormalization.