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Analytic renormalisation of the exponential interaction and weak interaction singularities

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Abstract

The parity non conserving interaction of a neutral vector meson with fermions is considered as a mathematical model suitable for investigating divergence problems of the weak interactions. Through the Stückelberg formalism and a canonical transformation the interaction is converted into an exponential form. The exponential interaction is studied, in the second order of perturbation theory, through the method of analytic renormalisation. Generalised amplitudes are introduced as localizable distributions depending on auxiliary complex parameters λ. It is shown that the distributions possess a nonisolated singularity at the physical point λ0. A method is developed for discarding the singularity thereby obtaining the physical amplitudes as localizable distributions which display a non-analytic dependence on the coupling constant.

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Authors and Affiliations

  1. Department of Theoretical Physics, Oxford, England

    P. K. Mitter

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  1. P. K. Mitter
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Mitter, P.K. Analytic renormalisation of the exponential interaction and weak interaction singularities. Commun.Math. Phys. 20, 251–267 (1971). https://doi.org/10.1007/BF01646622

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  • DOI: https://doi.org/10.1007/BF01646622

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