Abstract
We revisit via a path-integral approach the magnetic top proposed recently by Barut, Božić, and Marić. We point out that the magnetic top has the SU(2) symmetry and that it can be viewed as a free top seen from a rotating frame. We present an alternative path-integral quantization of the magnetic top on the basis of the symmetry, and show that the magnetic coupling does not participate in altering the spin quantum numbers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
W. Pauli, Z. Phys. 31, 765 (1925).
G. E. Uhlenbeck and S. Goudsmit, Naturwissenschaften 13, 953 (1925); Nature 117, 264 (1926).
See, e.g., M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966), p. 133.
W. Pauli, in Handbuch der Physik, H. Geiger and K. Sheel, eds., Vol. 24, Part 1 (Springer, Berlin, 1933), p. 126.
A. H. Compton, J. Franklin Inst. 192, 145 (1921).
F. Reiche, Z. Phys. 39, 444 (1926).
H. Casimir, “Rotation of a rigid body in quantum mechanics,” Thesis, Leyden and Groningen, 1931; Proc. Roy. Acad. Amsterdam 34, 844 (1931).
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).
L. S. Schulman, Phys. Rev. 176, 1558 (1968); Techniques and Applications of Path Integration (Wiley, New York, 1981).
A. M. Polyakov, Mod. Phys. Lett. A3, 325 (1988).
S. Kitakado, in ISATQM-Shanxi’ 92, J. Q. Liang, M. L. Wang, S. N. Qiao, and D. C. Su, eds. (Science Press, Beijing, 1993), p. 90.
A. O. Barut, M. Božić, and Z. Marić, Ann. Phys. (N.Y.) 214, 53 (1992).
A. O. Barut and I. H. Duru, Phys. Lett. A 158, 441 (1991).
See, e.g., H. Goldstein, Classical Mechanics, 2nd edn. (Addison-Wesley, Reading, Massachusetts, 1980), p. 143.
This type of transformations has been used in D. Peak and A. Inomata, J. Math. Phys. 10, 1422 (1969). J. M. Cai, P. Y. Cai, and A. Inomata, in ISATQM-Shanxi’ 92, J. Q. Liang, M. L. Wang, S. N. Qiao, and D. C. Su, eds. (Science Press, Beijing,), p. 75.
G. Junker and A. Inomata, in Path Integrals from meV to MeV, M. C. Gutzwiller, A. Inomata, J. R. Klauder, and L. Streit, eds. (World Scientific, Singapore, 1986), p. 315. C. Grosche and F. Steiner, Z. Phys. C 36, 699 (1987).
M. Böhm and G. Junker, J. Math. Phys. 28, 1978 (1987).
A. Inomata, H. Kuratsuji, and C. C. Gerry, Path Integrals and Coherent States of SU(2) and SU(1, 1) (World Scientific, Singapore, 1992).
W. Langguth and A. Inomata, J. Math. Phys. 20, 499 (1979).
Lectures of A. O. Barut and C. Piron in the Edirne Conference on Frontiers of Theoretical Physics (1993).
Private conversation with the first author (A.I.) in Minsk, Belarus, 1994.
Rights and permissions
About this article
Cite this article
Inomata, A., Junker, G. & Rosch, C. Remarks on the Magnetic Top. Foundations of Physics 28, 729–739 (1998). https://doi.org/10.1023/A:1018893619066
Issue Date:
DOI: https://doi.org/10.1023/A:1018893619066