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Title of Journal: Gen Relativ Gravit

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Abbravation: General Relativity and Gravitation

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Springer-Verlag

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DOI

10.1016/0169-5002(90)90289-X

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1572-9532

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Observables in a noncommutative approach to the un

Authors: Leszek Pysiak Michael Heller Zdzisław Odrzygóźdź Wiesław Sasin
Publish Date: 2005/03/24
Volume: 37, Issue: 3, Pages: 541-555
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Abstract

We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in Gen Rel Grav 36 111–126 2004 Generalized symmetries of the model are defined by a groupoid Γ given by the action of a finite group on a space E The geometry of the model is constructed in terms of suitable noncommutative algebras on Γ We investigate observables of the model especially its position and momentum observables This is not a trivial thing since the model is based on a noncommutative geometry and has strong nonlocal properties We show that in the position representation of the model the position observable is a coderivation of a corresponding coalgebra “coparallelly” to the wellknown fact that the momentum observable is a derivation of the algebra We also study the momentum representation of the model It turns out that in the case of the algebra of smooth quickly decreasing functions on Γ the model in its “quantum sector” is nonlocal ie there are no nontrivial coderivations of the corresponding coalgebra whereas in its “gravity sector” such coderivations do exist They are investigated

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