[math-ias] REMINDER: Members Seminar -- TODAY (Monday, November 12, 2012)

[Dottie Phares]

INSTITUTE FOR ADVANCED STUDY

School of Mathematics

Princeton, NJ  08540

 

 
                 REMINDER:
 
                    Members Seminar
 

 

                        Topic:                       Proof of a 35 Year Old
Conjecture for the Entropy of SU(2) 

                                                        Coherent States and
its Generalization

 

                              Speaker:                   Elliot Lieb,
Princeton University
 
                        Date/Time/Room:      November 12, 2012, 2:00pm -
3:00pm/S-101
 

Abstract:  35 years ago Wehrl defined a classical entropy of a quantum
density matrix using Gaussian 

(Schr\"odinger, Bargmann, ...) coherent states. This entropy, unlike other
classical approximations, has 

the virtue of being positive. He conjectured that the minimum entropy occurs
for a density matrix that

is itself a projector onto a coherent state and this was proved about a year
later. It was then conjectured 

that the same thing would occur for SU(2) coherent states (maximal weight
vectors in a representation 

of SU(2)). This conjecture, and a generalization of it, have now been proved
with J.P. Solovej. (arxiv: 1208.3632). 

After a review of coherent states in general, a summary of the proof will be
given. Obviously, one would like 

to prove similar conjectures for SU(n) and other Lie groups. This is open
and the audience is invited to join the 

fun. Another question the audience is invited to think about is the meaning
of all this for group representation 

theory.  If this conjecture is correct, it must have some general
significance

 

 

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