On Mar 9, 2012, at 11:30 PM, JACK SARFATTI wrote:

above case of Messina's paper this is

P(1)B = (1/2)(1 + e^-2<n(t)>A)

P(0)B = (1/2)(1 + e^-2<n(t)>A)

Of course, if one continues to think of this as Born probability, ad-hoc renormalization gives 1/2, 1/2 same as in ordinary QM.

i.e. take

P'(1)B = P(1)B/[P(1)B + P(0)B] = 1/2

But the whole point here is that the Goldstone "phase rigidity" (P.W. Anderson's "More is different") of the Glauber coherent states is a complete breakdown of the Born probability rule. The P's above are not probabilities but are relative signal strengths and do not have to be renormalized to conserve probability.

The Glauber states are eigenstates of a non-Hermitian operator. The rule that quantum observables must be Hermitian operators is violated in this case. In addition Glauber states emerge from spontaneous symmetry breakdown - in this case a U1 symmetry relating boson number and conjugate phase. Indeed, the Glauber states are order parameters - displaced from the ordinary boson vacuum in phase space. Their time evolution is not unitary.