The Background Field Method as a Canonical Transformation

Abstract

We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is nothing but a direct field-theoretic generalization of the Lie transform of classical analytical mechanics, we comment on a number of possible applications, and in particular the non perturbative implementation of the background field method on the lattice, the background field formulation of the two particle irreducible formalism, and, finally, the formulation of the Schwinger-Dyson series in the presence of topologically non-trivial configurations.

11 pages, REVTeX. References added, some explanations extended. Final version to appear in the journal

References in corpus (5)

• Pinch Technique: Theory and Applications
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD
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Cited by in corpus (25)

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• Effects of divergent ghost loops on the Green's functions of QCD
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• Renormalization of gauge theories in the background-field approach
• Unified description of seagull cancellations and infrared finiteness of gluon propagators
• Gluon mass generation in the massless bound-state formalism
• Evidence of ghost suppression in gluon mass dynamics
• Background field method and nonlinear gauges
• AntiBRST symmetry and Background Field Method
• Gauge-covariant canonical formalism revisited with application to the proton spin decomposition
• QCD effective charge from the three-gluon vertex of the background-field method
• Gauge symmetry and background independence: Should the proton spin decomposition be path independent?
• Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization
• Gauge (in)dependence and background field formalism
• Gauge copies in the Landau-DeWitt gauge: a background invariant restriction
• Background field method and the cohomology of renormalization
• Canonical Flow in the Space of Gauge Parameters
• Schwinger-Dyson truncations in the all-soft limit: a case study
• The Stueckelberg Mechanism in the presence of Physical Scalar Resonances
• High-energy QCD evolution from BRST symmetry
• Patterns of gauge symmetry in the background field method
• Some reference formulas for the generating functions of canonical transformations
• Non-Abelian gauge theories with composite fields in the background field method
• High-energy QCD evolution from Slavnov-Taylor identity
• Unquenching the infrared sector of QCD