Proof of the Wehrl-type Entropy Conjecture for Symmetric SU(N) Coherent States

Elliott H. Lieb; Jan Philip Solovej

doi:10.1007/s00220-016-2596-9

Proof of the Wehrl-type Entropy Conjecture for Symmetric SU(N) Coherent States

Elliott H. Lieb, Jan Philip Solovej

Mathematics

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Abstract

The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group SU(2) , is further extended here to symmetric representations of the groups SU(N) for all N. This result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of Lie groups and their representations.

Original language	English (US)
Pages (from-to)	567-578
Number of pages	12
Journal	Communications In Mathematical Physics
Volume	348
Issue number	2
DOIs	https://doi.org/10.1007/s00220-016-2596-9
State	Published - Dec 1 2016

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group SU(2) , is further extended here to symmetric representations of the groups SU(N) for all N. This result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of Lie groups and their representations.",

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N2 - The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group SU(2) , is further extended here to symmetric representations of the groups SU(N) for all N. This result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of Lie groups and their representations.

AB - The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group SU(2) , is further extended here to symmetric representations of the groups SU(N) for all N. This result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of Lie groups and their representations.

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Proof of the Wehrl-type Entropy Conjecture for Symmetric SU(N) Coherent States

Abstract

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