Escuela de Física-Matemática 2011
Mikhail Malakhaltsev
(Departamento de Matemáticas, Universidad de Los Andes)
Hopf bundle and quantum mechanics
Heinz Hopf discovered the bundle, which nowadays is referred to as ``Hopf bundle'', in 1931, in order to calculate the homotopy group π3(S2). The Hopf bundle is a wonderful example of a principal bundle with rich geometry which appears in various geometrical situations. The aim of the talk is to demonstrate that Berry's phases can be described using the Hopf bundle of a Hilbert space.