Convolution of Ultradistributions, Field Theory, Lorentz Invariance and Resonances

C. G. BOLLINI, P. MARCHIANO AND M. C. ROCCA

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS

Springer

Año: 2007 vol. 46 p. 3030 - 3059

0020-7748

In this work, a general definition of convolution between twoarbitrary  Ultradistributions of Exponential type (UET) is given.The product of two arbitrary  UET is defined via the convolution of itscorresponding 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 inconfiguration space is obtained in both, Euclidean andMinkowskian spacesAs an application of our formalism, we givea solution to the question of normalization of resonances in Quantum Mechanics.General formulae for convolution of even, spherically symmetric and Lorentz invariant UETare obtained and several examplesof application are given.