Classical particles with internal structure: general formalism and application to first-order internal spaces.

Atre, MV and Mukunda, N (1986) Classical particles with internal structure: general formalism and application to first-order internal spaces. In: Journal of Mathematical Physics, 27 (12). pp. 2908-2919.

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Abstract

Classical relativistic particles with internal structure have been the subject of extensive studies. The theories involving group theory primarily consider the Poincar´e group as the underlying symmetry group and the internal space admits a transitive action of the Lorentz subgroup. The authors of this paper systematically classify such internal spaces under the requirement that each possible internal space Q is a coset space G/H; G = SL(2,C) and H is a continuous Lie subgroup of G. The set of all possible Q’s falls into two types: first-order spaces and second-order spaces, depending on whether a canonical description can be given using Q itself or if it needs the cotangent bundle T Q. The first type is discussed in detail in this paper and the second type is discussed in another of the authors’ papers [same journal 28 (1987), no. 4, 792–806]. Using the Kostant-Kirillov-Souriau theorem, it is further shown that there exist three possible first-order spaces; two are related respectively to the so-called generic and exceptional orbits in G, the orbits corresponding to two possible two-dimensional subgroups H; and the third is related to a two-fold covering of the exceptional orbit. The latter space corresponds to the use of a Majorana spinor as the internal variable, as discussed earlier by Mukunda, H. van Dam and L. C. Biedenharn [Phys. Rev. D (3) 22 (1980), no. 8, 1938–1951; MR0590397 (81k:81034); Biedenharn and Mukunda, ibid. D (3) 23 (1981), no. 6, 1451–1454]. The authors further develop for the former two internal spaces a Lagrangian description of a classical relativistic object and study the dynamics.

Item Type:	Journal Article
Publication:	Journal of Mathematical Physics
Publisher:	American Institute of Physics
Additional Information:	Copyright of this article belongs to American Institute of Physics.
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003) Division of Physical & Mathematical Sciences > Physics
Date Deposited:	21 Jul 2004
Last Modified:	10 Jan 2012 06:49
URI:	http://eprints.iisc.ac.in/id/eprint/975

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