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Born Reciprocity and the Granularity of Spacetime


Jarvis, PD and Morgan, SO, Born Reciprocity and the Granularity of Spacetime, Foundations of Physics Letters, 19, (6) pp. 501-517. ISSN 0894-9875 (2006) [Refereed Article]

DOI: doi:10.1007/s10702-006-1006-5


The Schrödinger-Robertson inequality for relativistic position and momentum operators X μ, P ν, μ, ν = 0, 1, 2, 3, is interpreted in terms of Born reciprocity and 'non-commutative' relativistic position-momentum space geometry. For states which saturate the Schrödinger-Robertson inequality, a typology of semiclassical limits is pointed out, characterised by the orbit structure within its unitary irreducible representations, of the full invariance group of Born reciprocity, the so-called 'quaplectic' group U(3, 1) #x2297;s H(3, 1) (the semi-direct product of the unitary relativistic dynamical symmetry U(3, 1) with the Weyl-Heisenberg group H(3, 1)). The example of the 'scalar' case, namely the relativistic oscillator, and associated multimode squeezed states, is treated in detail. In this case, it is suggested that the semiclassical limit corresponds to the separate emergence of spacetime and matter, in the form of the stress-energy tensor, and the quadrupole tensor, which are in general reciprocally equivalent.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other physical sciences
Research Field:Other physical sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
UTAS Author:Morgan, SO (Mr Stuart Morgan)
ID Code:41368
Year Published:2006
Funding Support:Australian Research Council (DP0208808)
Web of Science® Times Cited:16
Deposited By:Physics
Deposited On:2006-08-01
Last Modified:2010-06-18

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