Browsing by Subject "curved spacetime"

Quantum field theory is often presented without clearly defined mathematical structures, especially in the case of field operators. We discuss axiomatic quantum field theory, where quantum fields and states are defined rigorously using distribution theory, alongside their assumed properties in the form of the Wightman axioms. We present the two key results that come from this construction, namely CPT symmetry and the spin-statistics connection. We then consider the construction of quantum fields in curved spacetime so as to discuss their behaviour in regions of large curvature, such as near black holes. This requires us to redefine fields and states in terms of *-algebras. We then present the GNS reconstruction theorem which allows us to get back the original definitions of these objects in Minkowski spacetime.