5,397 research outputs found
On Isomorphism of "Functional" Intersection and Union Types
Type isomorphism is useful for retrieving library components, since a
function in a library can have a type different from, but isomorphic to, the
one expected by the user. Moreover type isomorphism gives for free the coercion
required to include the function in the user program with the right type. The
present paper faces the problem of type isomorphism in a system with
intersection and union types. In the presence of intersection and union,
isomorphism is not a congruence and cannot be characterised in an equational
way. A characterisation can still be given, quite complicated by the
interference between functional and non functional types. This drawback is
faced in the paper by interpreting each atomic type as the set of functions
mapping any argument into the interpretation of the type itself. This choice
has been suggested by the initial projection of Scott's inverse limit
lambda-model. The main result of this paper is a condition assuring type
isomorphism, based on an isomorphism preserving reduction.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework
A model-independent, locally generally covariant formulation of quantum field
theory over four-dimensional, globally hyperbolic spacetimes will be given
which generalizes similar, previous approaches. Here, a generally covariant
quantum field theory is an assignment of quantum fields to globally hyperbolic
spacetimes with spin-structure where each quantum field propagates on the
spacetime to which it is assigned. Imposing very natural conditions such as
local general covariance, existence of a causal dynamical law, fixed spinor- or
tensor-type for all quantum fields of the theory, and that the quantum field on
Minkowski spacetime satisfies the usual conditions, it will be shown that a
spin-statistics theorem hols: If for some spacetimes the corresponding quantum
field obeys the "wrong" connection between spin and statistics, then all
quantum fields of the theory, on each spacetime, are trivial.Comment: latex2e, 1 figure, 32 page
TQFT's and gerbes
We generalize the notion of parallel transport along paths for abelian
bundles to parallel transport along surfaces for abelian gerbes using an
embedded Topological Quantum Field Theory (TQFT) approach. We show both for
bundles and gerbes with connection that there is a one-to-one correspondence
between their local description in terms of locally-defined functions and forms
and their non-local description in terms of a suitable class of embedded
TQFT's.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-14.abs.htm
A classical approach to TQFT's
We present a general framework for TQFT and related constructions using the
language of monoidal categories. We construct a topological category C and an
algebraic category D, both monoidal, and a TQFT functor is then defined as a
certain type of monoidal functor from C to D. In contrast with the cobordism
approach, this formulation of TQFT is closer in spirit to the classical
functors of algebraic topology, like homology. The fundamental operation of
gluing is incorporated at the level of the morphisms in the topological
category through the notion of a gluing morphism, which we define. It allows
not only the gluing together of two separate objects, but also the self-gluing
of a single object to be treated in the same fashion. As an example of our
framework we describe TQFT's for oriented 2D-manifolds, and classify a family
of them in terms of a pair of tensors satisfying some relations.Comment: 72 pages, 7 figure
Algebraic Quantum Theory on Manifolds: A Haag-Kastler Setting for Quantum Geometry
Motivated by the invariance of current representations of quantum gravity
under diffeomorphisms much more general than isometries, the Haag-Kastler
setting is extended to manifolds without metric background structure. First,
the causal structure on a differentiable manifold M of arbitrary dimension
(d+1>2) can be defined in purely topological terms, via cones (C-causality).
Then, the general structure of a net of C*-algebras on a manifold M and its
causal properties required for an algebraic quantum field theory can be
described as an extension of the Haag-Kastler axiomatic framework.
An important application is given with quantum geometry on a spatial slice
within the causally exterior region of a topological horizon H, resulting in a
net of Weyl algebras for states with an infinite number of intersection points
of edges and transversal (d-1)-faces within any neighbourhood of the spatial
boundary S^2.Comment: 15 pages, Latex; v2: several corrections, in particular in def. 1 and
in sec.
Homogeneous coordinates for algebraic varieties
We associate to every divisorial (e.g. smooth) variety with only constant
invertible global functions and finitely generated Picard group a
-graded homogeneous coordinate ring. This generalizes the usual
homogeneous coordinate ring of the projective space and constructions of Cox
and Kajiwara for smooth and divisorial toric varieties. We show that the
homogeneous coordinate ring defines in fact a fully faithful functor. For
normal complex varieties with only constant global functions, we even
obtain an equivalence of categories. Finally, the homogeneous coordinate ring
of a locally factorial complete irreducible variety with free finitely
generated Picard group turns out to be a Krull ring admitting unique
factorization.Comment: 30 page
- …