ar X iv : h ep - t h / 93 11 11 2 v 1 1 9 N ov 1 99 3 Covariant differential complexes on quantum linear groups . ∗

ar X iv : h ep - t h / 93 11 07 1 v 1 1 1 N ov 1 99 3 COVARIANT QUANTIZATION OF GREEN SCHWARZ SUPERSTRING

We describe a canonical covariant approach to the quantization of the Green-Schwarz superstring. The approach is first applied to the canonical covariant quantization of the Brink and Schwarz superparticle. The Kallosh action is obtained in this case, with the correct BRST cohomology.

ar X iv : h ep - t h / 93 11 13 2 v 1 2 2 N ov 1 99 3 Quantum integrable systems and representations of Lie algebras

Introduction A quantum many particle system on the line with an interaction potential U (x) is defined by the Hamiltonian

ar X iv : h ep - t h / 93 11 06 9 v 1 1 1 N ov 1 99 3 QUANTUM GROUPS

These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in Decem-ber 1992. They constitute a brief and elementary introduction to quantum symmetries from a physical point of view, along the lines of the forthcoming book by C. Gómez, G. Sierra and myself.

ar X iv : h ep - t h / 94 11 03 9 v 1 5 N ov 1 99 4 DFTT - 44 / 94 November 1994 R - MATRIX FORMULATION OF THE QUANTUM INHOMOGENEOUS GROUPS

ar X iv : h ep - p h / 96 11 36 1 v 1 1 9 N ov 1 99 6 Relativistic quantum mechanics in the einbein field formalism

The system of two relativistic particles with einbein fields is quan-tized as a constrained system. A method of the introduction of the Newton–Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some arguments are involved in the favour of Lorents covariant gauge fixing conditions.