28,403 research outputs found
Representations of nets of C*-algebras over S^1
In recent times a new kind of representations has been used to describe
superselection sectors of the observable net over a curved spacetime, taking
into account of the effects of the fundamental group of the spacetime. Using
this notion of representation, we prove that any net of C*-algebras over S^1
admits faithful representations, and when the net is covariant under Diff(S^1),
it admits representations covariant under any amenable subgroup of Diff(S^1)
Laminations and groups of homeomorphisms of the circle
If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that
pi_1(M) acts on a circle. Here, we show that some other classes of essential
laminations also give rise to actions on circles. In particular, we show this
for tight essential laminations with solid torus guts. We also show that
pseudo-Anosov flows induce actions on circles. In all cases, these actions can
be made into faithful ones, so pi_1(M) is isomorphic to a subgroup of
Homeo(S^1). In addition, we show that the fundamental group of the Weeks
manifold has no faithful action on S^1. As a corollary, the Weeks manifold does
not admit a tight essential lamination, a pseudo-Anosov flow, or a taut
foliation. Finally, we give a proof of Thurston's universal circle theorem for
taut foliations based on a new, purely topological, proof of the Leaf Pocket
Theorem.Comment: 50 pages, 12 figures. Ver 2: minor improvement
The Computable Universe Hypothesis
When can a model of a physical system be regarded as computable? We provide
the definition of a computable physical model to answer this question. The
connection between our definition and Kreisel's notion of a mechanistic theory
is discussed, and several examples of computable physical models are given,
including models which feature discrete motion, a model which features
non-discrete continuous motion, and probabilistic models such as radioactive
decay. We show how computable physical models on effective topological spaces
can be formulated using the theory of type-two effectivity (TTE). Various
common operations on computable physical models are described, such as the
operation of coarse-graining and the formation of statistical ensembles. The
definition of a computable physical model also allows for a precise
formalization of the computable universe hypothesis--the claim that all the
laws of physics are computable.Comment: 33 pages, 0 figures; minor change
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