Nota de FísicaPublicado
SU(4) Properties of the Dirac-Kähler Equation
C.A. Linhares; Juan Alberto Mignaco
1991
Dados da publicação
- Autores
- C.A. Linhares; Juan Alberto Mignaco
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 1991
- Descrição
- We use the Dirac-Kähler formalism in the space of differential forms (endowed with a Clifford product) to study the SU(4) symmetry related to the description of spin-1/2 particles found previously in the usual matrix treatment. We show that differential forms may be taken as the generators spanning the algebra of the SU(4) group and how the operations of this group can be related to a change of frame of reference in the algebra. We demonstrate that minimal left ideals of the algebra constitute irreducible representations for spin-1/2 particles for Clifford operation from the left, and exhibit how these ideals are related via space inversion, time reversal and their product. We also consider the dual space of minimal right ideals and show how the Dirac-Kähler differential operator acts from the right, leaving the minimal right ideals invariant. This allows the introduction of an adjoint form and through the definition of a suitable scalar product, of conserved currents. We emphasize the relevance of all these features to the problem of proliferation of fermion species in the continuum limit of the lattice formalism.
- Ano
- 1991
- Número
- CBPF-NF-008/91
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não