Superselection Rule for Charge
The customary notion of superselection rule stipulates the vanishing of those matrix elements of the density matrix that connect states separated by the superselection rule, i.e., the relative phases of which are, according to the superselection rule, meaningless. It is shown that, if any two states for which an additive conserved quantity has different values are separated for all physical systems by a superselection rule at one time, the separation will persist for all times. It is concluded that the states with different electric (or baryonic) charges are so separated. The reason for the difference between electric charge and other additive conserved quantities, such as momentum, is brought out.
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- 1.R. Mirman, Phys. Rev. 186, 1380 (1969); V. Aharonov and L. Susskind, ibid. 155, 1428 (1967).Google Scholar
- 2.E. P. Wigner, in Physikertag. Hauptvortraege Jahrestag. Verbandes Deut. Physik. Ges. (Physik Verlag, \Iosbach/Baden, 1962). The superselection rule for electric charge was first proposed by G.-C. Wick, A. S. Wightman, and E. P. Wigner, Phys. Rev. 88, 101 (1952)Google Scholar
- 3.The reader who is familiar with (1), or is willing to take it for granted, should skip the present section.Google Scholar
- 4.Y. Aharonov and L. Susskind, Ref. 1. This article already contains the form (5) for the “permissible” density matrix.Google Scholar
- 5.Cf. Ref. 2.Google Scholar
- E. P. Wigner and M. Yanase, Proc. Natl. Acad. Sci. U. S. 49, 910 (196.3). The more general statement referred to in the Introduction (and Ref. 2) is that if, with respect to an additive conserved quantity, the skew information is zero to begin with, it will remain zero throughout.Google Scholar