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Dynamical groups and their currents

A model for strong interactions

  • Conference paper
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Current Algebra and Phenomenological Lagrange Functions

Part of the book series: Springer Tracts in Modern Physics 118 ((STMP,volume 50))

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Abstract

We have presented a discussion of the differences between the group structure of the multiplets and the group structure of interactions. We have also presented models in which these properties are explicitely exhibited. Because both the particle states and the currents are explicitely given not only sum rules but all matrix elements themselves are known. We have reviewed the general framework of the dynamical group theory, its special form in the case of the Dirac particle and the H-atom and its application to hadrons. The rest frame group O (4,2) emerges as the common and the most important ingredient in all three cases. Within this framework, the rest frame group, the particular representation of it, and the form of the quantum mechanical conserved current specify a particular physical system. We have also discussed a quantitative model for the hadrons, that describe rather well (a) the mass spectrum, (b) the partial decay rates, (c) the magnetic moments, (d) the electromagnetic form factors and transition form factors, and (e) the diffraction scattering of hadrons.

There are problems which need further study. Among these we have mentioned (1 °) the inclusion of antiparticles and the form-factors in the time-like region, (2 °) a more general treatment of the scattering processes and of general crossing properties, (3 °) a deeper understanding of the tensorial properties of interactions with respect to the internal quantum numbers, and (4 °) a more fundamental basis for the several parameters which we have fitted so far using empirical information.

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Authors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    Prof. Dr. A. O. Barut

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  1. Prof. Dr. A. O. Barut
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Barut, A.O. (1969). Dynamical groups and their currents. In: Current Algebra and Phenomenological Lagrange Functions. Springer Tracts in Modern Physics 118, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0045914

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  • DOI: https://doi.org/10.1007/BFb0045914

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  • Print ISBN: 978-3-540-04713-1

  • Online ISBN: 978-3-540-36172-5

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