The structure of the quantum mechanical state space and induced superselection rules

S. S. Horushy, V. N. Sushko

Joachim Kupsch

The role of superselection rules for the derivation of classical probability within quantum mechanics is investigated and examples of superselection rules induced by the environment are discussed.

Jason Edward Bradshaw

Domenico Giulini

The process of dynamical decoherence may cause apparent superselection rules, which are sometimes called `environmentally induced' or `soft'. A natural question is whether such dynamical processes are eventually also responsible for at least some of the superselection rules which are usually presented as fundamentally rooted in the kinematical structure of the theory (so called `hard' superselection rules). With this question in mind, I re-investigate two well known examples where superselection rules are usually argued to rigorously exist within the given mathematical framework. These are (1) the Bargmann superselection rule for the total mass in Galilei invariant quantum mechanics and (2) the charge superselection rule in quantum electrodynamics. I argue that, for various reasons, the kinematical arguments usually given are not physically convincing unless they are based on an underlying dynamical process.

Fiona E. Harrison

K. Kong Wan

For orthodox quantum systems, pure states correspond one-to-one to all one-dimensional subspaces and observables correspond one-to-one to all selfadjoint operators in the state space. A relaxation of this one-to-one correspondence will bring about superselection rules. A general formulation of superselection rules is technically complicated. 1 We shall adopt an intuitive approach here and limit our discussion to some special cases to see how superselection rules can be incorporated in a Hilbert space structure of quantum theory.