β Scribed by Elihu Lubkin
No coin nor oath required. For personal study only.
0 ... 0 1, (Q, Qi form an additive system of quantities), if [Q, P] = 0 (superselection rule), and if the reduced density matrix pi is obtained from the density matrix P by tracing out over the j-spaces, j -f i, then [qi , pi] = 0. This shows that a superselection rule for an additive quantity propagates to subsystems. It is argued that superselection rules are therefore universal for additive quantities, unless a process of relativization with respect to a Q-reservoir is employed. Since such relativization is required to produce the coherent superpositions of momentum eigenstates needed for the notion of localization in position, it is argued that analogous processes of relativization can be used to break other superselection rules.
π SIMILAR VOLUMES
We reinvestigate Bargmann's superselection rule for the overall mass of n particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should be considered as a dynamical variable. We present a minimal ex