Non-Abelian monopoles break color. I. Classical mechanics

Balachandran, AP and Marmo, G and Mukunda, N and Nilsson, JS and Sudarshan, ECG and Zaccaria, F (1984) Non-Abelian monopoles break color. I. Classical mechanics. In: Physical Review D, 29 (12). pp. 2919-2935.

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Abstract

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Item Type:	Journal Article
Publication:	Physical Review D
Publisher:	American Physical Society
Additional Information:	Copyright for this article belongs to American Physical Society.
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited:	01 Feb 2010 06:54
Last Modified:	15 Dec 2018 05:31
URI:	http://eprints.iisc.ac.in/id/eprint/22894

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