Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-05-04
Int.J.Theor.Phys.46:3030-3059,2007
Physics
High Energy Physics
High Energy Physics - Theory
56 pages. Accepted for publication in International Journal of Theoretical Physics on June 19, 2006
Scientific paper
10.1007/s10773-007-9418-y
In this work, a general definition of convolution between two arbitrary Ultradistributions of Exponential type (UET) is given. The product of two arbitrary UET is defined via the convolution of its corresponding Fourier Transforms. Some examples of convolution of two UET are given. Expressions for the Fourier Transform of spherically symmetric (in Euclidean space) and Lorentz invariant (in Minkowskian space) UET in term of modified Bessel distributions are obtained (Generalization of Bochner's theorem). The generalization to UET of dimensional regularization in configuration space is obtained in both, Euclidean and Minkowskian spaces As an application of our formalism, we give a solution to the question of normalization of resonances in Quantum Mechanics. General formulae for convolution of even, spherically symmetric and Lorentz invariant UET are obtained and several examples of application are given.
Bollini C. G.
Marchiano P.
Rocca M. C.
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