# Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction

Igor Khavkine, Valter Moretti
December 18, 2014
Within this paper we introduce the overall idea of the algebraic formalism of QFT on a fixed globally hyperbolic spacetime in the framework of unital $*$-algebras. We point out some general features of CCR algebras, such as simplicity and the construction of symmetry-induced homomorphisms. For simplicity, we deal only with a real scalar quantum field. We discuss some known general results in curved spacetime like the existence of quasifree states enjoying symmetries induced from the background, pointing out the relevant original references. We introduce, in particular, the notion of a Hadamard quasifree algebraic quantum state, both in the geometric and microlocal formulation, and the associated notion of Wick polynomials.
open access link Chapter 5, Advances in Algebraic Quantum Field Theory, R. Brunetti et al. (eds.), Springer, 2015
@incollection{Khavkine:2014mta, author = "Khavkine, Igor and Moretti, Valter", title = "{Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction}", editor = "Brunetti, Romeo and Dappiaggi, Claudio and Fredenhagen, Klaus and Yngvason, Jakob", booktitle = "Advances in algebraic quantum field theory", journal = "Chapter 5, Advances in Algebraic Quantum Field Theory, R. Brunetti et al. (eds.), Springer, 2015", pages = "191-251", doi = "10.1007/978-3-319-21353-8_5", year = "2014", eprint = "1412.5945", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1412.5945;%%" }

Keywords:
quantum field theory on curved spacetimes