ar X iv : m at h / 04 10 55 1 v 2 [ m at h . D G ] 1 6 N ov 2 00 4 CLASSICAL FIELD THEORY ON LIE ALGEBROIDS : VARIATIONAL ASPECTS

ar X iv : m at h / 04 10 55 1 v 1 [ m at h . D G ] 2 6 O ct 2 00 4 CLASSICAL FIELD THEORY ON LIE ALGEBROIDS : VARIATIONAL ASPECTS

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-P...

ar X iv : m at h / 03 06 23 5 v 2 [ m at h . D G ] 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].

ar X iv : m at h / 04 10 61 1 v 2 [ m at h . A G ] 1 1 N ov 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES

ar X iv : m at h / 04 11 06 6 v 1 [ m at h . D G ] 3 N ov 2 00 4 QUANTISATION OF LIE - POISSON MANIFOLDS

In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and C∗-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid which deals with a big enough class of functions to include the above mentioned example. As an ...

ar X iv : m at h . D G / 0 30 62 35 v 2 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].