Regularization of theRepresentation
- 25 April 1969
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 180 (5), 1244-1255
- https://doi.org/10.1103/physrev.180.1244
Abstract
A representation is introduced for the density operator of the electromagnetic field that is suitable for all density operators and that reduces to the coherent-state representation when the latter exists. It expresses the density operator as the sum of four terms, each of which is a two-dimensional weighted integral over outer products of coherent states. The first integral has the form of the representation, i.e., the outer products are projection operators. The absence of singularities in this term is achieved by the presence of the three supplementary integrals which vanish when the density operator possesses the representation. In general, for stationary density operators, only the first two terms of the regularized representation are necessary. A simple prescription is given for obtaining the four weight functions of this representation from the function , where is a coherent state and is the density operator. According to this prescription, the representation does not exist and one or more of the supplementary, regularizing terms is necessary when the function contains a term that decreases more rapidly than as . The regularized representation affords nonsingular integral expressions for all density operators and for most expectation values, including, when they are finite, those of the normally ordered products of the creation and annihilation operators, and . The construction and use of this representation is illustrated with the aid of simple examples in which the density operator does not possess the representation.
Keywords
This publication has 28 references indexed in Scilit:
- Pure States and theRepresentationPhysical Review B, 1969
- Density Operators and Quasiprobability DistributionsPhysical Review B, 1969
- Ordered Expansions in Boson Amplitude OperatorsPhysical Review B, 1969
- Improved Version of Optical Equivalence TheoremPhysical Review Letters, 1966
- Relation between Quantum and Semiclassical Description of Optical CoherencePhysical Review B, 1965
- Coherence Properties of Optical FieldsReviews of Modern Physics, 1965
- Coherent and Incoherent States of the Radiation FieldPhysical Review B, 1963
- The Quantum Theory of Optical CoherencePhysical Review B, 1963
- Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light BeamsPhysical Review Letters, 1963
- Photon CorrelationsPhysical Review Letters, 1963