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Continuous-Representation Theory. I. Postulates of Continuous-Representation Theory
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.
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Cited by
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Zhang, W.-M., Feng, D. H., & Gilmore, R. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.867 · Cited by 1,521
Coherent states via decoherence.
Zurek, W. H., Habib, S., & Paz, J. P. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.1187 · Cited by 679
LargeNlimits as classical mechanics
Yaffe, L. G. (1982) · Reviews of Modern Physics · doi:10.1103/revmodphys.54.407 · Cited by 465
Multiphoton quantum optics and quantum state engineering
Dell’Anno, F., De Siena, S., & Illuminati, F. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.01.004 · Cited by 310
Dynamical Meaning of Quantum Adiabatic Phase: The Case of a Noncanonical System
Kuratsuji, H., & Iida, S. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.1003 · Cited by 41
Metadata
- Authors
- Klauder, J. R.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1963-08-01
- Volume
- 4
- Issue
- 8
- Pages
- 1055-1058
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2069056521
- Cited by
- 402
- References
- 0
- FWCI
- 3.93
- Type
- journal article
- Language
- en
- Open access
- closed
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