Within this chapter (published as ) 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.
- Pub Date:
- December 2014
- Mathematical Physics;
- General Relativity and Quantum Cosmology
- v3: better discussion of Unitary Equivalence, thanks to comments of Ko Sanders. v2: minor corrections, added reference to older work by Sahlmann and Verch. v1: 59 pages, 4 figures. arXiv admin note: text overlap with arXiv:1008.1776 by other authors