Continuous-Representation Theory. I. Postulates of Continuous-Representation Theory
John R. Klauder
Source abstract
In a continuous representation of Hilbert space, each vector ψ is represented by a complex, continuous, bounded function ψ(φ) ≡ (φ, ψ) defined on a set S of continuously many, nonindependent unit vectors φ having rather special properties: Each vector in S possesses an arbitrarily close neighboring vector, and the identity operator is expressable as an integral over projections onto individual vectors in S. In particular cases it is convenient to introduce labels for the vectors in S whereupon each ψ is represented by a complex, continuous, bounded, label-space function. Basic properties common to all continuous representations are presented, and some applications of the general formalism are indicated.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.