Mathematics

This is the first of two seminars concerning (noncommutative) geometric
methods in solid state physics. After reviewing some aspects of
Bloch-Floquet theory, which is used to diagonalise periodic Schrödinger
operators, I will introduce the so-called Bloch bundle, i.e. the
eigenbundle of the Hamiltonian. Restricting the physical dimension to
d<4 and imposing time-reversal symmetry, I will prove that the Bloch
bundle is trivial.
Based on: G. Panati, "Triviality of Bloch and Bloch-Dirac bundles", Ann.
H. Poicaré 8, 995 (2007).