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Constraint quantization of a worldline system invariant under reciprocal relativity: II

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Jarvis, PD and Morgan, SO (2008) Constraint quantization of a worldline system invariant under reciprocal relativity: II. Journal of Physics A: Mathematical and Theoretical, 41 (46). p. 465203. ISSN 1751-8113

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Abstract

We consider the worldline quantization of a system invariant under the symmetries of reciprocal relativity. Imposition of the first class constraint, the generator of local time reparametrizations, on physical states enforces identification of the worldline cosmological constant with a fixed value of the quadratic Casimir of the quaplectic symmetry group Q(3, I) ~ U(3, 1) ~ H(4), the semi-direct product of the pseudo-unitary group with the Weyl-Heisenberg group. In our previous paper, J. Phys. A: Math. Theor. 40 (2007) 12095, the 'spin' degrees of freedom were handled as covariant oscillators, leading to a unique choice of cosmological constant, required for projecting out negative-norm states from the physical gauge-invariant states. In the present paper, the spin degrees of freedom are treated as standard oscillators with positive norm states (wherein Lorentz boosts are not number-conserving in the auxiliary space; reciprocal transformations are of course not spin-conserving in general). As in the covariant approach, the spectrum of the square of the energy-momentum vector is continuous over the entire real line, and thus includes tachyonic (spacelike) and null branches. Adopting standard frames, the Wigner method on each branch is implemented, to decompose the; auxiliary space into unitary irreducible representations of the respective little algebras and additional degeneracy algebras. The physical state space is vastly enriched as compared with the covariant approach, and contains towers of integer spin massive states, as well as unconventional massless representations of continuous spin type, with continuous Euclidean momentum and arbitrary integer helicity.

Item Type: Article
Keywords: quantization worldline system invariant reciprocal relativity
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Page Range: p. 465203
ISSN: 1751-8113
Identification Number - DOI: 10.1088/1751-8113/41/46/465203
Additional Information: The definitive publisher authenticated version is available online at http://www.iop.org/EJ/journal/JPhysA
Date Deposited: 04 Feb 2009 00:18
Last Modified: 18 Nov 2014 03:55
URI: http://eprints.utas.edu.au/id/eprint/8285
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