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Remarks on local symmetry invariance in perturbative algebraic quantum field theory. (English) Zbl 1306.81137
Summary: We investigate various aspects of invariance under local symmetries in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result is the proof that the quantum Batalin-Vilkovisky operator, on-shell, can be written as the commutator with the interacting BRST charge. Up to now, this was proven only for a certain class of fields in quantum electrodynamics and in Yang-Mills theory. Our result is more general and it holds in a wide class of theories with local symmetries, including general relativity and the bosonic string. We also comment on other issues related to local gauge invariance and, using the language of homological algebra, we compare different approaches to quantization of gauge theories in the pAQFT framework.

##### MSC:
 81T15 Perturbative methods of renormalization applied to problems in quantum field theory 46L60 Applications of selfadjoint operator algebras to physics 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 83C47 Methods of quantum field theory in general relativity and gravitational theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81R15 Operator algebra methods applied to problems in quantum theory
pAQFT
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