Abstract
We propose a model of a spin particle as an analogue of a quantum mechanical top. We show that for this model, we can prove the theorem on the relation between spin and statistics in the framework of nonrelativistic quantum mechanics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Fierz, “Zum Problem der Anaphylaxie mit chemisch bekannten Substanzen,” Helv. Phys. Acta, 12, 3–17 (1939).
W. Pauli, “The connection between spin and statistics,” Phys. Rev., 58, 716–722 (1940).
W. Pauli, “Exclusion principle, Lorentz group, and reflection of space-time and charge,” in: Niels Bohr and the Development of Physics (W. Pauli, L. Rosenfeld, and V. Weisskopf, eds.), McGraw-Hill, New York (1955), pp. 30–51.
M. I. Petrashen and E. D. Trifonov, Applications of Group Theory in Quantum Mechanics [in Russian], URSS, Moscow (2016); English transl. prev. ed., Dover, Mineola, N. Y. (2013).
I. G. Kaplan, Intermolecular Interactions [in Russian], BINOM, Moscow (2014); English transl. prev. ed., Wiley, New York (2006).
I. S. Duck and E. C. G. Sudarshan, Pauli and the Spin-Statistics Theorem, World Scientific, Singapore (1997).
A. S. Wightman, “Pauli and the spin-statistics theorem,” Am. J. Phys., 67, 742–746 (1999).
A. Jabs, “Connecting spin and statistics in quantum mechanics,” Found. Phys., 40, 776–792 (2010); “Addendum to: Connecting spin and statistics in quantum mechanics. DOI 10.1007/s10701-009-9351-4,” Found. Phys., 40, 793–794 (2010).
E. D. Trifonov, “On the spin-statistics theorem,” Phys. Usp., 60, 621–622 (2017).
E. P. Wigner, Group Theory and Its Application to the Quantum Mehanics of Atomic Spectra (Pure Appl. Phys., Vol. 5), Acad. Press, New York (1959).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 3, Quantum Mechanics: Non-Relativistic Theory, Fizmatlit, Moscow (1989); English transl. prev. ed., Pergamon, London (1965).
A. S. Davydov, Quantum Mechanics [in Russian], Nauka, Moscow (1973); English transl. prev. ed., Pergamon, Oxford (1965).
M. A. Elyashevich, Atomic and Molecular Spectroscopy [in Russian], URSS, Moscow (2001).
I. M. Gel'fand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation Group and the Lorentz Group [in Russian], Fizmatlit, Moscow (1958); English transl.: Representations of the Rotation and Lorentz Groups and Their Applications, Macmillan, New York (1963).
H. A. Bethe, Intermediate Quantum Mechanics, Benjamin, New York (1964).
B. L. van der Waerden, “Exclusion principle and spin,” in: Theoretical Physics in the Twentieth Century (M. Fierz and V. F. Weisskopf, eds.), Interscience, New York (1960), pp. 199–244.
B. V. Medvedev, Basis of Theoretical Physics [in Russian], Moscow (2007).
Acknowledgments
The author is sincerely grateful to M. G. Benedict, A. A. Grib, L. N. Labzovsky V. P. Smirnov, A. S. Troshin, and A. V. Tulub for their interest in the work and their discussions and comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 199, No. 3, pp. 399–404, June, 2019.
Rights and permissions
About this article
Cite this article
Trifonov, E.D. Spin Top (Toward a Theorem on the Spin-Statistics Relation). Theor Math Phys 199, 823–827 (2019). https://doi.org/10.1134/S0040577919060047
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577919060047