20 research outputs found
Perturbative Construction of Models of Algebraic Quantum Field Theory
We review the construction of models of algebraic quantum field theory by
renormalized perturbation theory.Comment: 38 page
Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction
Within this chapter (published as [49]) 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.Comment: 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 author