A quasi-Lie bialgebra formulation of the Pohlmeyer-Rehren Poisson algebra

Details A quasi-Lie bialgebra formulation of the Pohlmeyer-Rehren Poisson algebra A quasi-Lie bialgebra formulation of the Pohlmeyer-Rehren Poisson algebra

2009-09-17

arxiv.org/abs/0909.3279v1

Travaux mathematiques. Vol. XVII, 87--100, Trav. Math., 17, Fac. Sci. Technol. Commun. Univ. Luxemb., Luxembourg, 2007

Mathematics

Quantum Algebra

8 pages, proceedings of the Poisson geometry 2006 conference

Scientific paper

We present a quasi-Lie bialgebra (QLBA) quantization problem which comes from an algebraic reformulation of the Nambu-Goto string theory and invariant charges by Pohlmeyer and Rehren. This QLBA structure depends on a symmetric bivector (coming from a Minkowski metric) and is built on the free Lie algebra on a finite dimensional vector space. We solve this problem when the bivector has rank 1 or 2.

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