Abstract
In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.
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References
Agarwal G S and Wolf E 1970Phys. Rev. D2 2161
Bargmann V 1961Commun. Pure Appl. Math. 14 187
Kano Y 1965J. Math. Phys. 6 1913
Klauder J R 1960Ann. Phys. (N. Y) 11 123
Klauder J R, McKenna J and Currie D G 1965J. Math. Phys. 6 733
Klauder J R 1966Phys. Rev. Lett. 16 534
Klauder J R and Sudarshan E C G 1968Fundamentals of Quantum Optics (New York: W A Benjamin), Ch. 8
Levinson N 1940Gap and Density Theorems AMS Colloquium Pub. Vol. 26, Ch. IV
Mehta C L and Sudarshan E C G 1965Phys. Rev. 138B 274
Mehta C L 1967Phys. Rev. Lett. 18 752
Paley R E A C and Wiener N 1934Fourier Transforms in the Complex Domain AMS Colloquium Publications Vol. 19, Ch. VI, VII
Pool J C T 1966J. Math. Phys. 7 66
Rocca F 1966Compt. Rend. 262 A547
Sudarshan E C G 1963Phys. Rev. Lett. 10 277
Sudarshan E C G 1969J. Math. Phys. Sci. 3 121
Weyl H 1931The Theory of Groups and Quantum Mechanics (New York: Dover), p. 274
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Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992.
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Mukunda, N., Sudarshan, E.C.G. New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation. Pramana - J. Phys. 10, 227–238 (1978). https://doi.org/10.1007/BF02872020
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DOI: https://doi.org/10.1007/BF02872020