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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
Authors/Creators:	Jarvis, PD and Morgan, SO
Keywords:	quantization worldline system invariant reciprocal relativity
Journal or Publication Title:	Journal of Physics A: Mathematical and Theoretical
ISSN:	1751-8113
DOI / ID Number:	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
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