Quantum Field Theory on Curved Backgrounds -- A Primer

Understand

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.