680 research outputs found
Coexistence in interval effect algebras
Motivated by the notion of coexistence of effect-valued observables, we give
a characterization of coexistent subsets of interval effect algebras
Sharp and fuzzy observables on effect algebras
Observables on effect algebras and their fuzzy versions obtained by means of
confidence measures (Markov kernels) are studied. It is shown that, on effect
algebras with the (E)-property, given an observable and a confidence measure,
there exists a fuzzy version of the observable. Ordering of observables
according to their fuzzy properties is introduced, and some minimality
conditions with respect to this ordering are found. Applications of some
results of classical theory of experiments are considered.Comment: 23 page
Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
We study Archimedean atomic lattice effect algebras whose set of sharp
elements is a complete lattice. We show properties of centers, compatibility
centers and central atoms of such lattice effect algebras. Moreover, we prove
that if such effect algebra is separable and modular then there exists a
faithful state on . Further, if an atomic lattice effect algebra is densely
embeddable into a complete lattice effect algebra and the
compatiblity center of is not a Boolean algebra then there exists an
-continuous subadditive state on
Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Effect algebras are a generalization of many structures which arise in
quantum physics and in mathematical economics. We show that, in every modular
Archimedean atomic lattice effect algebra that is not an orthomodular
lattice there exists an -continuous state on , which is
subadditive. Moreover, we show properties of finite and compact elements of
such lattice effect algebras
Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
We study twisted N=2 superconformal gauge theory on a product of two Riemann
surfaces Sigma and C. The twisted theory is topological along C and holomorphic
along Sigma and does not depend on the gauge coupling or theta-angle. Upon
Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological
B-model on C whose target is the moduli space MV of nonabelian vortex equations
on Sigma. The N=2 S-duality conjecture implies that the duality group acts by
autoequivalences on the derived category of MV. This statement can be regarded
as an N=2 counterpart of the geometric Langlands duality. We show that the
twisted theory admits Wilson-'t Hooft loop operators labelled by both electric
and magnetic weights. Correlators of these loop operators depend
holomorphically on coordinates and are independent of the gauge coupling. Thus
the twisted theory provides a convenient framework for studying the Operator
Product Expansion of general Wilson-'t Hooft loop operators.Comment: 50 pages, latex. v2: an erroneous statement about an analog of the
Hitchin fibration has been fixe
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