Abstract
In Abelian subalgebras of observables it is shown that the integral representations of states in terms of coherent states result from the indistinguishability of the quanta of the harmonic oscillator under consideration. It is argued that these integral representations contain a quantum de Finetti theorem on Bose-Fock space.
Similar content being viewed by others
References
Hudson, R. L. and Moody, G. R., Z. Wahrscheinlichkeitstheorie verw. Gebiete 33, 343 (1976).
Bach, A., Lett. Nuovo Cimento 43, 383 (1985).
Aldous, D. J., in Lecture Notes in Mathematics 1117, Springer, Berlin, 1985, pp. 1–198.
de Finetti, B., Ann. Inst. H. Poincaré 7, 1 (1937).
Feller, W., An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, New York, 1966.
Bach, A., Lett. Nuovo Cimento 43, 195 (1985).
Bach, A., Phys. Lett. 104A, 251 (1984).
Benczur, A., Studia Scientiarium Mathematicarum Hungarica 3, 451 (1968).
Bach, A., Phys. Lett. 111A, 356 (1985).
Glauber, R. J., Phys. Rev. Lett. 10, 84 (1963).
Sudarshan, E. C. G., Phys. Rev. Lett. 10, 277 (1963).
Miller, M. M. and Mishkin, E. A., Phys. Rev. 164, 1610 (1967).
Davis, E. B., Quantum Theory of Open Systems, Academic Press, New York, 1976.
Bach, A. and Lüxmann-Ellinghaus, U., Commun. Math. Phys. 107, 553 (1986).
Bach, A. and Lüxmann-Ellinghaus, U., Lett. Math. Phys. 9, 103 (1985).
Arecchi, F. T., Gilmore, R., and Kim, D. M., Lett. Nuovo Cimento 6, 219 (1972).
Jaynes, E. T., in P. K.Goel and A.Zellner (eds.), Bayesian Interference and Decision Techniques —Essays in Honour of Bruno de Finetti, North-Holland, Amsterdam, 1986, pp. 31–42.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bach, A. On the origin of the integral representations in quantum optics. Lett Math Phys 13, 237–244 (1987). https://doi.org/10.1007/BF00423451
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00423451