Generalizations of the Born-Infeld Model and Exact Solutions

DIEGO JULIO CIRILO

Lambert Academic Publishing

Año: 2010 p. 136

3843358230

Group theory and geometry play an increasing important role in modern theoretical and mathematical physics. Using the theory of the Lie groups as unifying vehicle, the Born-Infeld (BI) theory is reformulated. New non-abelian supersymmetric models, concepts and results of the BI theory in several fields of physics are expressed in an extremely economical way. Regular exact solutions of the BI theory in curved space-time within this mathematical framework are presented. Non-abelian super-generalization of the BI action independent of the gauge group are proposed in a language where the endomorphism algebras can replace the concept of principal fiber bundle and the gauge theories are included in the Riemannian structure. Finally, starting from the superparticle and the string models, the quantum problem of the theories with reparameterization invariant actions is analyzed, the mathematical tools involved are presented and the hints for the further quantum tretment of more complicated theories (e.g. d-branes) are given. The corresponding physical states and new relativistic wave equation from these toy models with they relation with the Harmonic Oscillator are shown on several examples