Atre, MV and Mukunda, N (1987) Classical particles with internal structure. II. Second-order internal spaces. In: Journal of Mathematical Physics, 28 (4). pp. 792-806.
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A systematic study of classical relativistic particles with internal structure, initiated in a previous paper, is continued and a study of second-order internal spaces (SOS) is presented within the framework of the Lagrangian form of constrained dynamics. Such internal spaces Q are those for which a phase-space treatment must necessarily use the cotangent bundle T*Q. The large variety of possible SOS's-ten discrete cases and two one-parameter families-is separated into those capable of a manifestly covariant description, and those for which special methods based on the transitive action of SL(2,C) on a coset space are needed. The concept of the isotopy representation plays an important role in this context. Seven of the possible discrete SOS's are shown to be describable in a manifestly covariant way; two discrete and one one-parameter family of SOS's are shown to be unphysical in the sense that no Lagrangians can be written in which the internal and the space-time position variables are nontrivially coupled; and the remaining single discrete and one one-parameter family are shown to be physical though not describable in a manifestly covariant way. General phase-space methods uniformly applicable to all SOS's are developed; and as an illustrative example a Lagrangian model for an SOS in which the internal space is spanned by two orthonormal spacelike unit vectors is presented. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to American Institute of Physics.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Centre for Theoretical Studies|
|Date Deposited:||01 Sep 2004|
|Last Modified:||10 Jan 2012 06:26|
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