Thermodynamics in the NC disc

Abstract

We study the thermodynamics of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. We explicitly obtain expressions for thermodynamic potentials of gases of particles obeying different statistics. In order to do that, we derive an asymptotic expansion for the density of the zeros of Laguerre polynomials. As a result we prove that the Bose-Einstein condensation in the noncommutative disc does not take place.arXiv:1803.05821v1 [hep-th]

The beauty of curved momentum space

“…The beauty of curved momentum space S. A. Franchino-Viñas Indeed, one immediately notices from this expression that the divergence is due not to the contribution of high energy modes; instead, it is a consequence of the integration domain being unbounded. One could argue that for compact noncommutative manifolds, such as the fuzzy disc or fuzzy sphere [37,40,42,43], the generalized uncertainty principle induced by the noncommuting coordinates forces the number of available states to be finite. In our present case, however, the underlying classical manifold is noncompact; therefore, even if there should exist a minimal area, the noncompactness of the manifold creates a bypass and allows the presence of an infinite number of states.…”

The beauty of curved momentum space

“…A. Franchino-Viñas Indeed, one immediately notices from this expression that the divergence is due not to the contribution of high energy modes; instead, it is a consequence of the integration domain being unbounded. One could argue that for compact noncommutative manifolds, such as the fuzzy disc or fuzzy sphere [37,40,42,43], the generalized uncertainty principle induced by the noncommuting coordinates forces the number of available states to be finite. In our present case, however, the underlying classical manifold is noncompact; therefore, even if there should exist a minimal area, the noncompactness of the manifold creates a bypass and allows the presence of an infinite number of states.…”

Massive Neutron Stars and White Dwarfs as Noncommutative Fuzzy Spheres

“…It was shown that in the presence of NC, the spacetime metric alters [37], causing the event horizon to shift and the singularity at the centre of a black hole to vanish, which is replaced by a regular de-Sitter core [38][39][40]. It further alters some other properties associated with black holes, such as the stability of Cauchy horizon [41], mini black hole formation with the central singularity replaced by a self-gravitating droplet [42], the Hawking temperature [43]. Various researchers also utilised this NC to describe a variety of other phenomena, including Berry curvature, fundamental length-scale, Landau levels, gamma-ray bursts, and many more [44][45][46][47][48][49].…”