4.4 Conclusions and Outlook
The generally covariant treatment of QFT discussed in this paper is based on the first principle that ensures equivalence of observable algebras based on isometric regions of different space-times. That’s all one needs to proceed, at the conceptual level. Important developments are those connected to the works of Hollands and Wald, Verch, Hollands, Ruzzi, and one easily foresees applications of the framework to interesting situations, such as those related to AdS space-time, or in general theories on space-times with boundaries, to the exploitation of the renormalization group at the algebraic level and its possible use towards a clarification of the role of the conformal anomaly in the treatment of theories on asymptotically AdS space-times. Another, perhaps more important topic, is that related to background independent formulation of perturbative quantum gravity. We hope to report on these soon.
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Ausculta fili verba magistri Benedetto (480–547), incipit from “Regola”. Dedicated to Jacques Bros
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Brunetti, R. (2007). Locally Covariant Quantum Field Theories. In: de Monvel, A.B., Buchholz, D., Iagolnitzer, D., Moschella, U. (eds) Rigorous Quantum Field Theory. Progress in Mathematics, vol 251. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7434-1_4
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