30,662 research outputs found
Domain Representable Spaces Defined by Strictly Positive Induction
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 space is a topological space characterized by
its strong representability over domains. In this paper, we study strictly
positive inductive definitions for spaces by means of domain
representations, i.e. we show that there exists a canonical fixed point of
every strictly positive operation on 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
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
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
- …