Algebraic methods proved to be very successful in the context of quantum field theory on curved spacetimes. A quantum theory could be also understood as an assignment of an algebra of observables on the spacetime and an algebraic state, which is a positive, linear and normalized functional on the algebra of observables. In the first part of the talk, we outline a reason why algebraic states should be determinated nonlocally by the geometry, studying the abelian Chern-Simons theory formulated in the algebraic approach. Thereafter, we propose a `global’ construction for Dirac fields in the Rindler spacetime, using functional analytic techniques. In the two dimensional setting, we construct both ground and thermal states, while in four dimensions we obtain new quantum states.

 
org: GIULIANI Alessandro