Dynamical locality of the free scalar field
The paper under review deals with the fundamental question of when a theory describes the same physics on all spacetimes (SPAS). The authors state a conceptual frame and analyze the conditions on a theory that ensure that its physical content is the same in a large class of spacetimes. Mathematically, the question is studied in the framework of locally covariant quantum field theories as developed by \textit{R. Brunetti} et. al [Commun. Math. Phys. 237, No. 1--2, 31--68 (2003; Zbl 1047.81052)]. Concretely, any quantum field theory defined in all spacetimes is modelled by a functor between the category of globally hyperbolic manifolds and the category of C*-algebras. The authors propose the following principles that should be satisfied on a class \(\mathcal{T}\) of theories describing the same physics on all spacetimes (SPASs): (S1) Every theory should be locally covariant. (S2) If \(\mathcal{A}\) and \(\mathcal{B}\) are theories in \(\mathcal{T}\) with \(\mathcal{A}\) a sub-theory of \(\mathcal{B}\), and \(\mathcal{A}\) and \(\mathcal{B}\) coincide in one spacetime, then they should coincide in all spacetimes. The authors show by explicit constructions that the full class of locally covariant theories does not have the property of describing the same physics on all spacetimes. They also introduce the notion of dynamically local theories, that means theories whose dynamical and kinematical local structures coincide. It is shown in Theorem~6.10 that this class of theories fulfill the SPASs property. As an application, the authors give in this context a model independent proof of the impossibility of making a covariant choice of a preferred state in all spacetimes. The article is clearly written, both from the physical and mathematical point of view. It contains a long and informative introduction. See also the authors paper [ibid. 13, No. 7, 1613--1674 (2012; Zbl 1280.81099)].
locally covariant quantum field theories
quantum field theory on curved spacetimes
scientific article