BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Quantum geometry of 3-dimensional lattices - Bazhanov\, V (Austral
 ian National)
DTSTART:20090327T100000Z
DTEND:20090327T110000Z
UID:TALK17556@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We study geometric consistency relations between angles on 3-d
 imensional (3D) circular quadrilateral lattices -- lattices whose faces ar
 e planar quadrilaterals inscribable into a circle. We show that these rela
 tions generate canonical transformations of a remarkable ``ultra-local'' P
 oisson bracket algebra defined on discrete 2D surfaces consisting of circu
 lar quadrilaterals. Quantization of this structure leads to new solutions 
 of the tetrahedron equation (the 3D analog of the Yang-Baxter equation). T
 hese solutions generate an infinite number of non-trivial solutions of the
  Yang-Baxter equation and also define integrable 3D models of statistical 
 mechanics and quantum field theory. The latter can be thought of as descri
 bing quantum fluctuations of lattice geometry. The classical geometry of t
 he 3D circular lattices arises as a stationary configuration giving the le
 ading contribution to the partition function in the quasi-classical limit.
LOCATION:Seminar Room 1 Newton Institute
END:VEVENT
END:VCALENDAR