82 research outputs found
Remarks on Local Symmetry Invariance in Perturbative Algebraic Quantum Field Theory
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
Lorentzian Wetterich equation for gauge theories
In a recent paper, with Drago and Pinamonti we have introduced a
Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using
the algebraic approach to perturbative QFT. The equation governs the flow of
the average effective action, under changes of a mass parameter k. Here we
introduce an analogous flow equation for gauge theories, with the aid of the
Batalin-Vilkovisky (BV) formalism. We also show that the corresponding average
effective action satisfies an extended Slavnov-Taylor identity in Zinn-Justin
form. We interpret the equation as a cohomological constraint on the functional
form of the average effective action, and we show that it is consistent with
the flow.Comment: 42 page
QFT on curved spacetimes : axiomatic framework and examples
In this review article we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self contained introduction into the framework, which should be accessible for both physicists and mathematicians
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