2013/11/30 by Damiano Anselmi
Mathematics · Physics and Astronomy · #BRST quantization #Background field method #Black Holes and Theoretical Physics #Completeness (order theory) #Cosmology and Gravitation Theories #Formalism (music) #Gauge theory #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Parametric statistics #Physics #Quantum field theory #Renormalization #Supergravity #Supersymmetry #Theoretical physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.89.045004
published as Phys. Rev. D 89, 045004 (2014) · 40 pages; v2: minor changes, PRD version
arxiv created 2014/02/05 · openalex publication_date 2014/02/06 · arxiv updated 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the background field method with the Batalin-Vilkovisky formalism, to generalize known results, study the parametric completeness of general gauge theories and achieve a better understanding of several properties. In particular, we study renormalization and gauge dependence to all orders. Switching between the background field approach and the usual approach by means of canonical transformations, we prove parametric completeness without making use of cohomological theorems; namely we show that if the starting classical action is sufficiently general all divergences can be subtracted by means of parameter redefinitions and canonical transformations. Our approach applies to renormalizable and nonrenormalizable theories that are manifestly free of gauge anomalies and satisfy the following assumptions: the gauge algebra is irreducible and closes off shell, the gauge transformations are linear functions of the fields, and closure is field independent. Yang-Mills theories and quantum gravity in arbitrary dimensions are included, as well as effective and higher-derivative versions of them, but several other theories, such as supergravity, are left out.