30,662 research outputs found

    Domain Representable Spaces Defined by Strictly Positive Induction

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    Recursive domain equations have natural solutions. In particular there are domains defined by strictly positive induction. The class of countably based domains gives a computability theory for possibly non-countably based topological spaces. A qcb0 qcb_{0} space is a topological space characterized by its strong representability over domains. In this paper, we study strictly positive inductive definitions for qcb0 qcb_{0} spaces by means of domain representations, i.e. we show that there exists a canonical fixed point of every strictly positive operation on qcb0qcb_{0} spaces.Comment: 48 pages. Accepted for publication in Logical Methods in Computer Scienc

    A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework

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    We propose a gauge-independent mechanism for the area-law behavior of Wilson loop expectation values in terms of worldsheets spanning Wilson loops interacting with the spin foams that contribute to the vacuum partition function. The method uses an exact transformation of lattice-regularized Yang-Mills theory that is valid for all couplings. Within this framework, some natural conjectures can be made as to what physical mechanism enforces the confinement property in the continuum (weak coupling) limit. Details for the SU(2) case in three dimensions are provided in a companion paper.Comment: 16 pages, 4 figure

    Operator Algebras of Functions

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    We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar multipliers of a vector-valued reproducing kernel Hilbert space. We use these to further develop a quantized function theory for various domains that extends and unifies Agler's theory of commuting contractions and the Arveson-Drury-Popescu theory of commuting row contractions. We obtain analogous factorization theorems, prove that the algebras that we obtain are dual operator algebras and show that for many domains, supremums over all commuting tuples of operators satisfying certain inequalities are obtained over all commuting tuples of matrices.Comment: 33 page
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