Role of twisted statistics in the noncommutative degenerate electron gas

We consider the problem of a degenerate electron gas in the background of a uniformly distributed positive charge, ensuring overall neutrality of the system, in the presence of noncommutativity. In contrast to previous calculations [F. S. Bemfica and H. O. Girotti, J. Phys. A 38, L539 (2005)] that did not include twisted formalism, we study the effects of noncommutativity from the points of view of both usual and braided twisted symmetry. We find corrections to the ground-state energy already at first order in perturbation theory when the usual twisted statistics is taken into account. The effects of noncommutativity, however, disappears if braided twisted symmetry is considered. In the former case these corrections arise since the interaction energy is sensitive to two-particle correlations, which are modified for the usual twisted anticommutation relations.