2021/01/31 by Partha Nandi, Sankarshan Sahu, Sayan Kumar Pal
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Geometry #Landau quantization #Magnetic field #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Quantization (signal processing) #Quantum #Quantum field theory #Quantum mechanics #Rotational symmetry #Symmetry (geometry) #Symmetry breaking #Theoretical physics #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2021.115511
Title modified, minor changes, To be published in Nucl. Phys. B
openalex publication_date 2021/07/30 · arxiv created 2021/07/31 · arxiv updated 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A riveting study of Ward-Takahashi identities is presented for a broken dilatation or scale symmetry in a generalized quantum Hall system. 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. We then derive an expression for the unintegrated scale or dilatation anomaly for the generalized Landau system using Fujikawa's method and is subsequently renormalised. In fact, we identify the Ward-Takahashi identities associated with broken dilatation symmetry to be anomalous which is a purely quantum effect induced from the noncommutative structure between spatial coordinates and therefore non-intuitive in nature.