Lie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry
Abstract
In the first part we present the Weyl algebra and our results concerning its finitedimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of deformations and contractions of these algebraic structures. We then concentrate on a particular such Lie algebra of order 3 which extends in a nontrivial way the Poincaré algebra, this extension being different of the supersymmetric extension. We then focus on the construction of a field theoretical model based on this algebra, the {\it cubic supersymmetry} ({\it 3SUSY}). For this purpose we obtain bosonic multiplets with whom we construct invariant Lagrangians. We then study the compatibility between this new symmetry and the abelian gauge symmetry. Furthermore, the analyse of possible interactions shows that interactions terms are not allowed by the cubic supersymmetry invariance. Finally we establish results regarding the extension in arbitrary dimensions of our model.
 Publication:

Ph.D. Thesis
 Pub Date:
 September 2005
 arXiv:
 arXiv:hepth/0509174
 Bibcode:
 2005PhDT.......140T
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 168 pages, 3 figures, PhD thesis