9,226 research outputs found
Endomorphisms and automorphisms of locally covariant quantum field theories
In the framework of locally covariant quantum field theory, a theory is
described as a functor from a category of spacetimes to a category of
*-algebras. It is proposed that the global gauge group of such a theory can be
identified as the group of automorphisms of the defining functor. Consequently,
multiplets of fields may be identified at the functorial level. It is shown
that locally covariant theories that obey standard assumptions in Minkowski
space, including energy compactness, have no proper endomorphisms (i.e., all
endomorphisms are automorphisms) and have a compact automorphism group.
Further, it is shown how the endomorphisms and automorphisms of a locally
covariant theory may, in principle, be classified in any single spacetime. As
an example, the endomorphisms and automorphisms of a system of finitely many
free scalar fields are completely classified.Comment: v2 45pp, expanded to include additional results; presentation
improved and an error corrected. To appear in Rev Math Phy
Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions
We present new sufficient conditions for the existence of a continuous utility function for an arbitrary binary relation on a topological space. Such conditions are basically obtained by using both the concept of a weakly continuous binary relation on a topological space and the concept of a countable network weight. In particular, we are concerned with suitable topological notions which generalize the concept of compactness and do not imply second countability or local compactness.hereditarily Lindeloef space; weakly continuous binary relation; countable network weight; hemicompactness; submetrizability
Modular Theory, Non-Commutative Geometry and Quantum Gravity
This paper contains the first written exposition of some ideas (announced in
a previous survey) on an approach to quantum gravity based on Tomita-Takesaki
modular theory and A. Connes non-commutative geometry aiming at the
reconstruction of spectral geometries from an operational formalism of states
and categories of observables in a covariant theory. Care has been taken to
provide a coverage of the relevant background on modular theory, its
applications in non-commutative geometry and physics and to the detailed
discussion of the main foundational issues raised by the proposal.Comment: Special Issue "Noncommutative Spaces and Fields
- …