Quick Search:
Prog. Theor. Phys. Vol. 87 No. 1 (1992) pp. 61-76
The Wigner-Araki-Yanase Theorem and Its Extension in Quantam Measurement with Generalized Coherent States
Shoju Kudaka and
Kiyotaka Kakazu
Department of Physics, University of the Ryukyus, Okinawa 903-01
(Received July 25, 1991)
Abstract:
The relationship between the measurement of an operator and the presence of a conservation law is studied using generalized coherent states. It is shown that an operator which does not commute with a conserved quantity cannot be measured exactly; this is an extension of the theorem by Wigner, Araki and Yanase, expressing the conserved quantity in a more general form. Classical operators play an important role in this approach. We present a simple model of the approximate measurement of a particle-spin which does not commute with the (additive) conserved angular momentum. Also, using two other models we show that the condition of distinguishability of pointer-operators is consistent with the situation where the statistical operator in a physical system tends to just its mixed-part.
URL :
http://ptp.ipap.jp/link?PTP/87/61/
DOI : 10.1143/PTP.87.61
References:
- J. von Neumann, Die Mathematische Grundlagen der Quantenmechanik (Springer Verlag, Berlin, 1932).
- E. P. Wigner, Z. Phys. 131 (1952), 101.
-
H. Araki and M. Yanase, Phys. Rev. 120 (1960), 622[APS].
-
M. Yanase, Phys. Rev. 123 (1961), 666[APS].
-
M. Ozawa, Phys. Rev. Lett. 67 (1991), 1956[APS].
- S. Kudaka, S. Matsumoto and K. Kakazu, Prog. Theor. Phys. 82 (1989), 665[PTP].
- K. Kakazu, Prog. Theor. Phys. 84 (1990), 195[PTP].
K. Kakazu and S. Matsumoto, Phys. Rev. A42 (1990), 5903[APS].
- S. Kudaka and S. Matsumoto, in Symp. Found. Mod. Phys. 1990, ed. P. Lahti and P. Mittelstaedt (World Scientific, 1990), p. 190.
- K. Kakazu, Nuovo Cim. B, to be published.
- K. Kakazu, Nuovo Cim. B, to be published.
- K. Kakazu, Phys. Rev. A, to be published.
- K. Kakazu and A. Ogawa, Prog. Theor. Phys. 86 (1991), 943[PTP].
- J. R. Klauder and B. S. Skagerstam, Coherent States (World Scientific, 1985).
A. M. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986).
-
P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40 (1968), 411[APS].
W. M. Zhang, D. H. Feng and R. Gilmore, Rev. Mod. Phys. 62 (1990), 867[APS].
- Z. Maki, Prog. Theor. Phys. 82 (1989), 638[PTP].
-
L. G. Yaffe, Rev. Mod. Phys. 54 (1982), 407[APS].
-
R. J. Glauber, Phys. Rev. 131 (1963), 2766[APS].
-
R. Fukuda, Phys. Rev. A35 (1987), 8[APS];
ibid. A36 (1987), 3023[APS]; Prog. Theor. Phys. 81 (1989), 34[PTP]; in Proc. 3rd Int. Symp. Found. Quantum Mechanics, ed. S. Kobayashi, H. Ezawa, Y. Murayama and S. Nomura (Phys. Soc. Jpn, Tokyo, 1990), p. 124.
- K. Hepp, Helv. Phys. Acta 45 (1972), 237.
S. Machida and M. Namiki, in Proc. 1st Int. Symp. Found. Quantum Mechanics, ed. S. Kamefuchi, H. Ezawa, Y. Murayama, M. Namiki, S. Nomura, Y. Ohnuki and T. Tajima (Phys. Soc. Jpn., Tokyo, 1984), p. 136.
H. Nakazato and S. Pascazio, Phys. Lett. A156 (1991), 386.
- D. Bohm, Quantum Theory (Prentice-Hall, Inc., New York, 1951).
P. Busch and F. E. Schroeck, Jr., Found. Phys. 19 (1989), 807.
- W. Hu, Found. Phys. 20 (1990), 447.
