Adiabatic Regularization for Gauge Field and the Conformal Anomaly

Abstract

We construct the adiabatic regularization method for a $U(1)$ gauge field in a conformally flat spacetime by quantizing in the canonical formalism the gauge fixed $U(1)$ theory with mass terms for the gauge fields and the ghost fields. We show that the adiabatic expansion for the mode functions and the adiabatic vacuum can be defined in a similar way using WKB-type solutions as the scalar fields. As an application of the adiabatic method, we compute the trace of the energy momentum tensor and reproduces the known result for the conformal anomaly obtained by the other regularization methods. The availability of the adiabatic expansion scheme for gauge field allows one to study the renormalization of the de-Sitter space maximal superconformal Yang-Mills theory using the adiabatic regularization method.

arXiv comment22 pages. no figure. v2: ref added and typos corrected

References in corpus (13)

• Quantum Contributions to Cosmological Correlations
• Twenty Years of the Weyl Anomaly
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Adiabatic regularization and particle creation for spin one-half fields
• Renormalized stress-energy tensor for spin-1/2 fields in expanding universes
• de Sitter Supersymmetry Revisited
• Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space
• Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect
• AdS/dS CFT Correspondence
• Local momentum space and the vector field
• One-loop conformal anomaly in an implicit momentum space regularization framework
• Two-point function for the Maxwell field in flat Robertson-Walker spacetimes
• Topics in Quantum Field Theory in Curved Space

Cited by in corpus (12)

• The quantum fate of black hole horizons
• Energy-momentum tensor and helicity for gauge fields coupled to a pseudo-scalar inflaton
• The Thermal Bath of de Sitter from Holography
• Quantum Spacetime Instability and Breakdown of Semiclassical Gravity
• Instability of De Sitter Spacetime induced by Quantum Conformal Anomaly
• Maxwell field with gauge fixing term in de Sitter space: exact solution and stress tensor
• On the Flow of $\square R$ Weyl-Anomaly
• Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect
• Regularized stress tensor of vector fields in de Sitter space
• Argument for the radiation-dominated behavior of matter fields in the preinflationary era
• Maxwell field with gauge fixing term in the radiation- and matter-dominant stages: exact solution and stress tensor
• On Adiabatic Renormalization with a Physically Motivated Infrared Cut-Off