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arXiv · 1804.05782

Non-commutative waves for gravitational anyons

Sergio Inglima·Bernd Schroers
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Abstract

We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincaré symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We express the unitary irreducible representations in terms of covariant, infinite-component fields on curved momentum space satisfying algebraic spin and mass constraints. Adapting and applying the method of group Fourier transforms, we obtain covariant fields on (2+1)-dimensional Minkowski space which necessarily depend on an additional internal and circular dimension. The momentum space constraints turn into differential or exponentiated differential operators, and the group Fourier transform induces a star product on Minkowski space and the internal space which is essentially a version of Rieffel's deformation quantisation via convolution.

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Sergio Inglima, Bernd Schroers. 2018-12-22. Non-commutative waves for gravitational anyons. https://doi.org/10.1007/s11005-018-01148-6

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