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

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

Keywords:

quantum field theory on curved spacetimes