Abstract
Before the formalism of quantum theory was introduced, Bose and Einstein in 1924 and, without using this formalism, Fermi in 1925 introduced statistics for indistinguishable particles. Due to the fact, however, that indistinguishable particles were immediately incorporated into the new theory by Dirac in 1926, indistinguishability has always been considered as a typical quantum phenomenon which transcends classical conceptions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Jauch, J. M. 1968. Foundations of Quantum Mechanics. Reading: Addison-Wesley.
Girardeau, M. D. 1965. ‘Permutation Symmetry of Many-Particle Wave Functions’, Phys. Rev. 139 B500―B508.
Leinaas, J. M. and Myrheim, J. 1977. ‘On the Theory of Identical Particles’. Nuovo Cimento 37B 1–23.
Fleig, W. 1983. ‘On the Symmetry Breaking Mechanism of the Strong-Coupling BCS-Model’. Acta Physica Austriaca 55 135–153.
Ali, S. T. and Doebner, H. D. 1987. ‘Quantization, Topology and Ordering. In The Physics of Phase Space, ed. by Y. S. Kim and W. W. Zachary, Lecture Notes in Physics 278, Berlin: Springer, pp. 330–346.
Bach, A 1988. ‘The Concept of Indistinguishable Particles in Classical and Quantum Physics’. Found. Phys. 18 639–649.
Aldous, D. 1985. ’Exchangeability and Related Topics. In Ecole d’Eté de Probabilités de Saint-Flour XIII, P. L. Hennequin, Lecture Notes in Mathematics 1117, Berlin: Springer, pp. 1―198.
Brillouin, L. 1931. Die Quantenstatistik. Berlin: Springer.
von Misés, R. 1964. ‘Über Aufteilungs- und Besetzungswahrscheinlichkeiten’.In Selected papers of Richard von Mises, ed. by Ph. Frank et al., Providence: AMS, pp. 313―334.
Coleman, A. J. 1963. ‘Structure of Fermion Density Operators’. Rev. Mod. Phys. 35 668―689.
Feller, W. 1966. An Introduction to Probability Theory and its Applications, Vol. 2. New York: Wiley.
Bach, A. 1988. ‘Integral Representations for Indistinguishable Classical Particles: Brillouin Statistics. Phys. Lett. dA 129 440–442.
Benczur, A. 1968. ‘On Sequences of Equivalent Events and the Compound Poisson Process’. Stud. Sci. Math. Hung. 2 451–458.
Bach, A. 1989. ‘On the Statistics of Nonclassical Photon States’. Phys. Lett. A 134 405―408.
Hudson, R. L. and Moody, G. R. 1976. ‘Locally Normal Symmetric States and an Analogue of de Finetti’s Theorem’. Z. Wahrscheinlichkeitstheorie verw. Gebiete 33 343―351.
Accardi, L. Foundations of Quantum Mechanics: A Quantum Probabilistic Approach. Preprint, Rome.
Bach, A. and Lüxmann-Ellinghaus, 1986. ‘The Simplex Structure of the Classical States of the Quantum Harmonic Oscillator’. Commun. Math. Phys. 107 553–560.
Bach, A. 1988. ‘Quanta and Coherent States’, Lett. Math. Phys. 15 75―79.
Bach, A. 1987. ‘Integral Representations by Means of Coherent States Derived from de Finetti’s Theorem’. Europhys. Lett. 4 383–387.
Bach, A. and Srivastav, A. 1989. ‘A Characterization of the Classical States of the Quantum Harmonic Oscillator by Means of de Finetti’s Theorem’. Commun. Math. Phys. 123 453―462.
Walls, D. F. 1986. ‘Quantum Statistics of Nonlinear Optics’. In Frontiers of Nonequilibrium Statistical Physics, ed. by G. T. Moore and M. O. Scully, New York: Plenum, pp. 309―328.
Klauder, J. R. and Sudarshan, E. C. G. 1968. Fundamentals of Quantum Optics. New York: Benjamin.
Boltzmann, L. 1909. ‘Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung, respektive den Sätzen über das Wärmegleichgewicht’. In L. Boltzmann, Wissenschaftliche Abhandlungen, ed by F. Hasenöhrl Vol. 2. J. A. Barth, Leipzig, pp. 164–223.
Natanson, L. 1911. ‘Über die statistische Theorie der Strahlung’. Phys. Zs. 12 659―666.
Bose, S. N. 1924. ‘Plancks Gesetz und Lichtquantenhypothese’. Z. Phys. 26 178–181.
Planck, M. 1900. ‘Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum’. Verh. d. Deutsch. Phys. Ges. (2) 2 237―245.
Maddox, J. 1987. ‘Telling One Particle from Another’. Nature 329 579.
Bach, A. 1985. ‘On the Quantum Properties of Indistinguishable Classical Particles’. Lett. Nuovo Cimento 43 383–387.
Feynman, R. P. 1961. The theory of fundamental processes. New York: Benjamin.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publishers
About this chapter
Cite this chapter
Bach, A. (1990). Indistinguishability, Interchangeability, and Indeterminism. In: Cooke, R., Costantini, D. (eds) Statistics in Science. Boston Studies in the Philosophy of Science, vol 122. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0619-8_9
Download citation
DOI: https://doi.org/10.1007/978-94-009-0619-8_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6765-2
Online ISBN: 978-94-009-0619-8
eBook Packages: Springer Book Archive