Continuous-Representation Theory. I. Postulates of Continuous-Representation Theory
- 1 August 1963
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 4 (8) , 1055-1058
- https://doi.org/10.1063/1.1704034
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.Keywords
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