2015/09/20 by David J. Toms, Toms, David J.
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Differential Geometry Research #Algorithm #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Curvature #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry #Heat kernel #High Energy Physics - Theory (hep-th) #Kernel (algebra) #Lagrangian #Mathematical analysis #Mathematical physics #Mathematics #Minimal coupling #Minimal model #Minimal surface #Physics #Pure mathematics #Quantization (signal processing) #Quantum mechanics #Space (punctuation) #Vector field #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1509.05989
arxiv created 2015/09/20 · openalex publication_date 2015/09/20 · arxiv updated 2015/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The local momentum space method is used to study the quantized massive vector field (the Proca field) with the possible addition of non-minimal terms. Heat kernel coefficients are calculated and used to evaluate the divergent part of the one-loop effective action. It is shown that the naive expression for the effective action that one would write down based on the minimal coupling case needs modification. We adopt a Faddeev-Jackiw method of quantization and consider the case of an ultrastatic spacetime for simplicity. The operator that arises for non-minimal coupling to the curvature is shown to be non-minimal in the sense of Barvinsky and Vilkovisky. It is shown that when a general non-minimal term is added to the theory the result is not renormalizable with the addition of a local Lagrangian counterterm.