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Ternary Z3-graded Generalization of Heisenberg's Algebra

R. Kerner

Université Pierre & Marie Curie, Paris VI



Аннотация: Many Z2-graded algebraic structures can be generalized to the case of Z3-grading. Several such structures are presented: the Grassmann algenra, algebra of exterior forms, lie algebras. In the latter, the antisymmetric binary product is replaced by ternary Z3-skew symmetric product. Ternary Heisenberg algebra is then introduced and its Bogolyubov symmetry group established. The second quantization of this structure is introduces, and the sixth-order Hamiltonian defined, along with its eigenstates. The Bohr-Sommerfeld quantization is applied to the stationary periodic solutions and the eigenvalues of energy are computed.

Язык доклада: английский


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