Escuela de Física-Matemática 2010
Andrés Reyes (Universidad de los Andes, Bogotá):
Canonical group quantization and self-adjoint generators of symmetries
(Andrés' presentation)

Canonical group quantization is a quantization method developed by C. Isham that makes use of tools from geometric quantization and from the theory of induced representations. It emphasizes greatly the role of canonical commutation relations, making it particularly appealing from the physical point of view. From the mathematical point of view, it involves the construction of suitable representations, as self-adjoint operators, of the infinitesimal generators of the so-called canonical group. In this talk I will discuss two recent applications of the method. The first one is of experimental relevance in the field of quantum optics. The second one is concerned with the problem of quantum indistinguishability and the connection between spin and statistics.