2012/09/28 by Sergey N. Solodukhin · 19 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Factorization #Gauge boson #Gauge fixing #Gauge theory #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum entanglement #Quantum mechanics #Regularization (linguistics) #cond-mat.stat-mech #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep12(2012)036
published in Journal of High Energy Physics 2012(12) (Springer Nature) · 15 pages; v2: typos in eqs. (31), (32), (34), (36) corrected; discussion in section 6 expanded
arxiv created 2012/09/28 · openalex publication_date 2012/12/01 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
A bstract We analyze the dependence of the effective action and the entanglement entropy in the Maxwell theory on the gauge fixing parameter a in d dimensions. For a generic value of a the corresponding vector operator is nonminimal. The operator can be diagonalized in terms of the transverse and longitudinal modes. Using this factorization we obtain an expression for the heat kernel coefficients of the nonminimal operator in terms of the coefficients of two minimal Beltrami-Laplace operators acting on 0- and 1-forms. This expression agrees with an earlier result by Gilkey et al. Working in a regularization scheme with the dimensionful UV regulators we introduce three different regulators: for transverse, longitudinal and ghost modes, respectively. We then show that the effective action and the entanglement entropy do not depend on the gauge fixing parameter a provided the certain ( a -dependent) relations are imposed on the regulators. Comparing the entanglement entropy with the black hole entropy expressed in terms of the induced Newton’s constant we conclude that their difference, the so-called Kabat’s contact term, does not depend on the gauge fixing parameter a . We consider this as an indication of gauge invariance of the contact term.