Geodesic
Describing spinors using probability distribution functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 185-198 
V. I. Man'ko; O. V. Man'ko; S. S. Safonov. Describing spinors using probability distribution functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 185-198. http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a2/
@article{TMF_1998_115_2_a2,
     author = {V. I. Man'ko and O. V. Man'ko and S. S. Safonov},
     title = {Describing spinors using probability distribution functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {185--198},
     year = {1998},
     volume = {115},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a2/}
}
TY  - JOUR
AU  - V. I. Man'ko
AU  - O. V. Man'ko
AU  - S. S. Safonov
TI  - Describing spinors using probability distribution functions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1998
SP  - 185
EP  - 198
VL  - 115
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a2/
LA  - ru
ID  - TMF_1998_115_2_a2
ER  - 
%0 Journal Article
%A V. I. Man'ko
%A O. V. Man'ko
%A S. S. Safonov
%T Describing spinors using probability distribution functions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1998
%P 185-198
%V 115
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a2/
%G ru
%F TMF_1998_115_2_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Irreducible representations of the rotation group are realized using a family of positive probability distributions of the spin projections for an arbitrary value of the spin. The family is parametrized by the points on the sphere. An invertible mapping of the spinors onto the probability distribution functions is constructed. Examples of probability distributions for the well-known states with the spins $1/2$ and $1$ are presented.

[1] J. Bertrand, P. Bertrand, Found. Phys., 17 (1989), 397 | DOI | MR

[2] K. Vogel, H. Risken, Phys. Rev. A, 40 (1989), 2847 | DOI

[3] E. Wigner, Phys. Rev., 40 (1932), 749 | DOI | Zbl

[4] S. Mancini, V. I. Man'ko, P. Tombesi, Quantum Semiclass. Opt., 7 (1995), 615 | DOI

[5] G. M. D'Ariano, S. Mancini, V. I. Man'ko, P. Tombesi, Quantum Semiclass. Opt., 6 (1996), 1017 | DOI

[6] S. Mancini, V. I. Man'ko, P. Tombesi, Phys. Lett. A, 213 (1996), 1 ; Classical-like description of quantum dynamics by means of symplectic tomography, Los Alamos Preprint E-print quant-ph/9609026 | DOI | MR | Zbl

[7] S. Mancini, V. I. Man'ko, P. Tombesi, Found. Phys., 27 (1997), 801 | DOI | MR

[8] V. I. Man'ko, “Quantum mechanics and classical probability theory”, Proceedings of International conference “Symmetrics in Science IX” (Bregenz, Austria, August 1996), eds. B. Gruber and M. Ramek, Plenum Press, N. Y., 1997, 215 | MR

[9] J. E. Moyal, Proc. Cambridge Philos. Soc., 45 (1949), 99 | DOI | MR | Zbl

[10] V. V. Dodonov, V. I. Man'ko, Phys. Lett. A, 229 (1997), 335 | DOI | MR | Zbl

[11] V. I. Manko, O. V. Manko, ZhETF, 112:3 (1997), 796 | MR

[12] O. V. Man'ko, “Tomography of spin states and classical formulation of quantum mechanics”, Proceedings of International conference “Symmetrics in Science X” (Bregenz, Austria), eds. B. Gruber and M. Ramek, Plenum Press, N. Y., 1998 | MR

[13] O. V. Man'ko, J. Russ. Laser Res., 17 (1996), 439 ; Phys. Lett. A, 228 (1997), 29 | DOI | DOI | MR | Zbl

[14] V. I. Manko, S. S. Safonov, YaF, 61:4 (1998), 658 | MR

[15] L. C. Biedenharn, J. D. Louck, Angular momentum in quantum physics. Theory and application, Encyclopedia of mathematics and its applications, 8, Addison-Wesley, Reading, MA, 1981 | MR | Zbl

[16] D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, Nauka, M., 1970 | MR | Zbl

[17] A. N. Leznov, M. V. Savelev, Gruppovye metody integrirovaniya nelineinykh dinamicheskikh sistem, Nauka, M., 1985 | MR | Zbl

[18] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Nauka, M., 1989 | MR