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World-line quantization of a reciprocally invariant system

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

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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, θ(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 Q(D−1,1)∼=U(D−1, 1) H(D), 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 θ(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.

Item Type: Article
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Publisher: IOP Publishing Ltd
Page Range: pp. 12095-12111
ISSN: 1751-8113
Identification Number - DOI: 10.1088/1751-8113/40/40/006
Date Deposited: 07 Apr 2008 14:40
Last Modified: 18 Nov 2014 03:35
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