Convolution of ultradistributions, field theory, Lorentz invariance and resonances
International Journal of Theoretical Physics, 2007•Springer
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 …
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 …
Abstract
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.
Springer
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