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Seminários do IMPA

Teoria de Representações

Color Lie (super)algebras and Z2 × Z2 symmetries in the Levi-Leblond equation.
Zhanna Kuznetsova

Sexta-feira, 25 de maio de 2018, 15:30
Sala 228

We investigate systems with color Lie (super) algebra symmetries. In the first part of the talk I give a brief introduction in color Lie algebras and superalgebras focusing on the Z2*Z2 particular case.  In the second part I present an analysis of the symmetry operators of the Levy-Leblond equation which is a nonrelativistic wave equation of a spin 1/2 particle (nonrelativistic analog of the Dirac equation).  It is shown that the equation has two kinds of symmetries. One is given by the super Schroedinger algebra and the other one by a Z2×Z2 graded Lie superalgebra. The realization of the Z2*Z2 superalgebra is presented in terms of matrix differential operators.