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Born Reciprocity and the Granularity of Spacetime
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.
Funding
Australian Research Council
History
Publication title
Foundations of Physics LettersVolume
19Issue
6Pagination
501-517ISSN
0894-9875Department/School
School of Natural SciencesPublisher
Springer/Plenum PublishersPlace of publication
New York, USARepository Status
- Restricted