The Particle Structure of the Quantum Mechanical Bose and Fermi Gas

Bach A, Zessin HN (2017)
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 52(1): 14-29.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In the framework of von Neumann's description of measurements of discrete quantum observables we establish a one-to-one correspondence between symmetric statistical operators W of quantum mechanical systems and classical point processes kappa(W), thereby giving a particle picture of indistinguishable quantum particles. This holds true under irreducibility assumptions if we fix the underlying complete orthonormal system. The method of the Campbell measure is developed for such statistical operators; it is shown that the Campbell measure of a statistical operator W coincides with the Campbell measure of the corresponding point process kappa(W). Moreover, again under irreducibility assumptions, a symmetric statistical operator is completely determined by its Campbell measure. Themethod of the Campbell measure then is used to characterize Bose-Einstein and Fermi-Dirac statistical operators. This is an elementary introduction into the work of Fichtner and Freudenberg [10, 11] combined with the quantum mechanical investigations of [2] and the corresponding point process approach of [30]. It is based on the classical work of von Neumann [22], Segal, Cook and Chaiken [7, 8, 28] as well as Moyal [18].
Stichworte
Point process; Campbell measure; statistical operator
Erscheinungsjahr
2017
Zeitschriftentitel
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
Band
52
Ausgabe
1
Seite(n)
14-29
ISSN
1068-3623
eISSN
1934-9416
Page URI
https://pub.uni-bielefeld.de/record/2910385

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Bach A, Zessin HN. The Particle Structure of the Quantum Mechanical Bose and Fermi Gas. Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) . 2017;52(1):14-29.
Bach, A., & Zessin, H. N. (2017). The Particle Structure of the Quantum Mechanical Bose and Fermi Gas. Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) , 52(1), 14-29. doi:10.3103/S1068362317010034
Bach, A., and Zessin, H. N. (2017). The Particle Structure of the Quantum Mechanical Bose and Fermi Gas. Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 52, 14-29.
Bach, A., & Zessin, H.N., 2017. The Particle Structure of the Quantum Mechanical Bose and Fermi Gas. Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) , 52(1), p 14-29.
A. Bach and H.N. Zessin, “The Particle Structure of the Quantum Mechanical Bose and Fermi Gas”, Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) , vol. 52, 2017, pp. 14-29.
Bach, A., Zessin, H.N.: The Particle Structure of the Quantum Mechanical Bose and Fermi Gas. Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) . 52, 14-29 (2017).
Bach, A., and Zessin, Hans Norbert. “The Particle Structure of the Quantum Mechanical Bose and Fermi Gas”. Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 52.1 (2017): 14-29.

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