Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization

Abstract

We investigate the background field method with the Batalin-Vilkovisky formalism, to generalize known results, study parametric completeness 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 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 non-renormalizable 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.

40 pages; v2: minor changes, PRD version

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• Renormalization of Lorentz violating theories
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Cited by in corpus (14)

• Super-renormalizable & Finite Gravitational Theories
• Renormalization of Horava Gravity
• Universally Finite Gravitational & Gauge Theories
• The Ultraviolet Behavior Of Quantum Gravity
• Renormalization of gauge theories in the background-field approach
• Finite quantum gauge theories
• Lorentz-violating Yang-Mills theory: discussing the Chern-Simons-like term generation
• Weighted power counting and chiral dimensional regularization
• Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories
• Relational Symplectic Groupoid Quantization for Constant Poisson Structures
• Background independence in gauge theories
• Adler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories
• Background field method and the cohomology of renormalization
• Ward identities and gauge independence in general chiral gauge theories