2016/07/31 by Chris L. Lin, Carlos R. Ordóñez, Carlos Ordońẽz +1
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Boson #Computer science #Cosmology and Gravitation Theories #Cutoff #Fermi Gamma-ray Space Telescope #Fermion #Geometry #Jacobian matrix and determinant #Mathematical physics #Mathematics #Physics #Quantum mechanics #Regularization (linguistics) #Scaling #Statistical Mechanics and Entropy #cond-mat.quant-gas #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.94.085001
published as Phys. Rev. D 94, 085001 (2016) · 10 pages (this version is the published version)
openalex publication_date 2016/10/03 · arxiv created 2016/10/04 · arxiv updated 2016/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We regulate in Euclidean space the Jacobian under scale transformations for two-dimensional nonrelativistic fermions and bosons interacting via contact interactions and compare the resulting scaling anomalies. For fermions, Grassmannian integration inverts the Jacobian; however, this effect is canceled by the regularization procedure and a result similar to that of bosons is attained. We show the independence of the result with respect to the regulating function, and show the robustness of our methods by comparing the procedure with an effective potential method using both cutoff and \ensuremathζ-function regularization.