562 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
On the residual finiteness of outer automorphisms of relatively hyperbolic groups
We show that every virtually torsion-free subgroup of the outer automorphism
group of a conjugacy separable relatively hyperbolic group is residually
finite. As a direct consequence, we obtain that the outer automorphism group of
a limit group is residually finite.Comment: 11 pages, 1 figure. Section 3 is replaced by Theorem 1.3. More
detailed arguments. Added new references. To appear in Journal of Pure and
Applied Algebr
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