# Quantum Field Theory on Curved Backgrounds -- A Primer

June 03, 2013

Goal of this review is to introduce the algebraic approach to quantum field
theory on curved backgrounds. Based on a set of axioms, first written down by
Haag and Kastler, this method consists of a two-step procedure. In the first
one, a suitable algebra of observables is assigned to a physical system, which
is meant to encode all algebraic relations among observables, such as
commutation relations, while, in the second step, one must select an algebraic
state in order to recover the standard Hilbert space interpretation of a
quantum system. As quantum field theories possess infinitely many degrees of
freedom, many unitarily inequivalent Hilbert space representations exist and
the power of such approach is the ability to treat them all in a coherent
manner. We will discuss in detail the algebraic approach for free fields in
order to give to the reader all necessary information to deal with the recent
literature, which focuses on the applications to specific problems, mostly in
cosmology.

Keywords:

quantum field theory on curved spacetimes, algebraic quantum field theory