Symplectic formalism in conformal field theory. (English) Zbl 1050.81061

Schwarz, Albert

Connes, A. (ed.) et al., Quantum symmetries/ Symétries quantiques. Proceedings of the Les Houches summer school, Session LXIV, Les Houches, France, August 1 - September 8, 1995. Amsterdam: North-Holland (ISBN 0-444-82867-2/hbk). 957-977 (1998).

This is a short review of a rigorous mathematical formalism allowing one to establish a symplectic structure in the classical field theory models, staritng from the Lagrangian formulation of the models. The formalism may be developed in such a way that the temporal and spatial variables appear on equal footing. As an example, the known Chern-Simons model is considered. Then, the formalism is specially adjusted to conformal field theory models, and to superconformal ones as well, which is preceded by a review of the superconformal geometry.
For the entire collection see [Zbl 0902.00046].

Reviewer: Boris A. Malomed (Tel Aviv)

MSC:

81T40	Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
37J05	Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53D05	Symplectic manifolds (general theory)
81T60	Supersymmetric field theories in quantum mechanics

Keywords:

Lagrangian; supersymmetry; Chern-Simons model