Talk:Glauber–Sudarshan P representation

Exponent 2?
I understand that you are saying that the Glauber-Sudarshan P-Representation is one in which one looks at density matrices which are mixtures of coherent states. Right? But what is the significance of the exponent "2" over the "d" in the integral? JRSpriggs 06:07, 26 August 2006 (UTC)


 * It is shorthand for $$ \rm{d[Im(} \alpha)] \rm{d[Re(} \alpha)]$$, since $$ \alpha $$ is complex. If you think it is confusing the way it is, you can write it out explicitly. Waxigloo 14:04, 26 August 2006 (UTC)


 * This makes it sound like &alpha; is just a complex number. But it must actually be an element of an infinite dimensional space, which space is a subset of the set of functions from R3&times;{-1,+1} to the complex numbers (and that is only the real photons, not the virtual ones). JRSpriggs 07:47, 27 August 2006 (UTC)


 * It is just a complex number. The basis is the coherent state basis, which are completely characterized by a single complex number.Waxigloo 20:30, 27 August 2006 (UTC)

Changing the Title
Calling this representation Glauber-Sudarshan seems unreasonable, since Sudarshan discovered it first (see the references). Also Glauber in his paper acknowledges that Sudarshan got it first, yet renames it to P-representation.

Glauber argues (Sec. X) that the "P-function" must be positive, and criticizes Sudarshan for letting it be negative for quantum effects. In this case Glauber is wrong, the function is only positive for classical light. Hence the classical correspondence theorem. It cannot be strictly positive for quantum effects.

I think the representation should be called Sudarshan-Glauber representation. Sudarshan discovered it and Glauber popularized it. —Preceding unsigned comment added by 66.90.165.130 (talk) 20:36, 16 August 2008 (UTC)

Berezin Lieb inequalites
This is what in the mathematics literature is called the upper symbol of rho in connection with the Berezin-Lieb inequalities. See, for example, http://arxiv.org/abs/1106.5966

Bsimonca (talk) 18:22, 7 June 2013 (UTC)Barry Simon (Caltech)

Question about density matrix with coherent states
What is the meaning of rho(alpha, alpha')? Is this just  ? If so, this definitely needs to be stated explicitly. — Preceding unsigned comment added by 98.14.192.201 (talk) 03:51, 26 March 2014 (UTC)