K\"ahler Representation Theory
Bryan W. Roberts, Nicholas J. Teh
TL;DR
This paper demonstrates that Jordan-Lie-Banach algebras, which abstractly characterize quantum theory, can be represented as smooth functions on K"ahler manifolds, linking algebraic and geometric formulations of quantum mechanics.
Contribution
It establishes a canonical representation of Jordan-Lie-Banach algebras as smooth functions on K"ahler manifolds, bridging algebraic and geometric approaches in quantum theory.
Findings
Jordan-Lie-Banach algebras can be represented on K"ahler manifolds
Provides a geometric realization of quantum algebraic structures
Links algebraic quantum theory with differential geometry
Abstract
We show that Jordan-Lie-Banach algebras, which provide an abstract characterization of quantum theory equivalent to C^* algebras, can always be canonically represented in terms of smooth functions on a K\"ahler manifold.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Quantum Mechanics and Applications · Advanced Topics in Algebra