2012/01/09 by Daniele Binosi, D. Binosi, Andrea Quadri +1 · 14 citations
Mathematics · Physics and Astronomy · #Background field method #Black Holes and Theoretical Physics #Canonical transformation #Group (periodic table) #Instanton #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Quantum mechanics #Renormalization #Renormalization group #Transformation (genetics) #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.85.085020
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 85(8) (American Physical Society) · 24 pages, 1 figure
arxiv created 2012/01/09 · openalex publication_date 2012/04/18 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that for an SU(N) Yang-Mills theory the classical background-quantum splitting is nontrivially deformed at the quantum level by a canonical transformation with respect to the Batalin-Vilkovisky bracket associated with the Slavnov-Taylor identity of the theory. This canonical transformation acts on all the fields (including the ghosts) and antifields; it uniquely fixes the dependence on the background field of all the one-particle irreducible Green's functions of the theory at hand. The approach is valid both at the perturbative and nonperturbative level, being based solely on symmetry requirements. As a practical application, we derive the renormalization group equation in the presence of a generic background and apply it in the case of an SU(2) instanton. Finally, we explicitly calculate the one-loop deformation of the background-quantum splitting in lowest order in the instanton background.