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World-line quantization of a reciprocally invariant system

Citation

Goverts, J and Jarvis, PD and Morgan, SO and Low, SG, World-line quantization of a reciprocally invariant system, Journal of Physics A: Mathematical and Theoretical, 40, (40) pp. 12095-12111. ISSN 1751-8113 (2007) [Refereed Article]

DOI: doi:10.1088/1751-8113/40/40/006

Abstract

We present the world-line quantization of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on 'phase-space coordinates' (xμ(τ), pμ(τ)) which preserve the Minkowski metric and the symplectic form, and global shifts in these coordinates, together with coordinate-dependent transformations of an additional compact phase coordinate, (τ)). The action is that of free motion over the corresponding Weyl-Heisenberg group. Imposition of the first class constraint, the generator of local time reparametrizations, on physical states enforces identification of the world-line cosmological constant with a fixed value of the quadratic Casimir of the quaplectic symmetry group , the semi-direct product of the pseudo-unitary group with the Weyl-Heisenberg group (the central extension of the global translation group, with central extension associated with the phase variable (τ)). The spacetime spectrum of physical states is identified. Even though for an appropriate range of values the restriction enforced by the cosmological constant projects out negative norm states from the physical gauge invariant spectrum, leaving over spin zero states only, in this purely bosonic setting the mass-squared spectrum is continuous over the entire real line and thus includes a tachyonic branch as well. © 2007 IOP Publishing Ltd.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other Physical Sciences
Research Field:Physical Sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Physical Sciences
Author:Jarvis, PD (Dr Peter Jarvis)
Author:Morgan, SO (Mr Stuart Morgan)
ID Code:48965
Year Published:2007
Web of Science® Times Cited:8
Deposited By:Physics
Deposited On:2007-08-01
Last Modified:2008-04-04
Downloads:0

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