Remarks on noncommutativity and scale anomaly in planar quantum mechanics
Year: 2021
Type: preprint
Abstract: A study of a riveting connection between noncommutativity and the anomalous scale or dilatation symmetry is presented for a generalized quantum Hall system due to time dilatation transformations. On using the Peierls substitution scheme, it is shown that noncommutativity between spatial coordinates emerges naturally at a large magnetic field limit. Thereafter, we derive a path-integral action for the corresponding noncommutative quantum system and discuss the equivalence between the considered noncommutative system and the generalized Landau problem thus rendering an effective commmutative description. By exploiting the path-integral method due to Fujikawa, we derive an expression for the unintegrated scale or dilatation anomaly for the generalized Landau system, wherein the anomalies are identified with Jacobian factors arising from measure change under scale transformation and is subsequently renormalised. In fact, we derive exact expressions of anomalous Ward identities from which one may point out the existence of scale anomaly which is a purely quantum effect induced from the noncommutative structure between spatial coordinates.
Source: arXiv (Cornell University)
Authors: Partha Nandi, Sankarshan Sahu, Sayan Kumar Pal
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3125815743