NDLI: Convolution of n-Dimensional Tempered Ultradistributions and Field Theory

Content Provider	Springer Nature Link
Author	Bollini, C. G. Rocca, M. C.
Copyright Year	2004
Abstract	In this work, a general definition of convolution between two arbitrary tempered ultradistributions is given. When one of the tempered ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. In the four-dimensional case, when the tempered ultradistributions are even in the variables k $^{0}$ and ρ, we obtain an expression for the convolution, which is more suitable for practical applications. The product of two arbitrary even (in the variables x $^{0}$ and r) four-dimensional distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. With this definition of convolution, we treat the problem of singular products of Green Functions in Quantum Field Theory (for Renormalizable as well as for nonrenormalizable theories). Several examples of convolution of two tempered ultradistributions are given. In particular, we calculate the convolution of two massless Wheeler's propagators and the convolution of two complex mass Wheeler's propagators.
Starting Page	59
Ending Page	76
Page Count	18
File Format	PDF
ISSN	00207748
Journal	International Journal of Theoretical Physics
Volume Number	43
Issue Number	1
e-ISSN	15729575
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2004-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Physics Quantum Physics Mathematical and Computational Physics Elementary Particles, Quantum Field Theory
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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