by D R Bes (CNEA-Buenos Aires) & J Kurchan (CNEA-Buenos Aires)

These lecture notes deal with the problem of collective coordinates in many-body systems, which are treated as gauge systems in (0+1) dimensions. The resulting classical Dirac brackets are discussed, as well as the structure of the quantal space of wavefunctions. Emphasis is made on the application of the BRST formalism. Several systems displaying an approximate breakdown of symmetries are treated. Many-body physicists may find attractive both a rigorous formulation of the problem of collective coordinates and being introduced to the BRST formalism, which has become a fundamental tool in gauge theories. Field-theorists may find illuminating the applications to simpler mechanical examples. The notes are self-contained. In particular, they do not require a previous knowledge of either the BRST formalism or of collective transformations.

• Introduction
• The Classical Treatment of Systems Described by Means of Collective Coordinates
• The Hilbert Spaces Associated with Collective Coordinates
• The BRST Treatment
• The Quantification Procedure of Faddeev-Popov
• The Breaking and the Restoration of Symmetries
• The Application of the BRST Formalism to Abelian Transformations
• The Rotational Transformations in Three Dimensions
• The Collective Dynamics