Symplectic Dirac-Kähler Fields

Details Symplectic Dirac-Kähler Fields Symplectic Dirac-Kähler Fields

1999-10-09

arxiv.org/abs/hep-th/9910085v1

J.Math.Phys. 40 (1999) 5593-5640

Physics

High Energy Physics

High Energy Physics - Theory

86 pages, latex

Scientific paper

10.1063/1.533048

For the description of space-time fermions, Dirac-K\"ahler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase-spaces. Rather than on space-time, symplectic Dirac-K\"ahler fields can be defined on the classical phase-space of any Hamiltonian system. They are equivalent to an infinite family of metaplectic spinor fields, i.e. spinors of Sp(2N), in the same way an ordinary Dirac-K\"ahler field is equivalent to a (finite) mulitplet of Dirac spinors. The results are interpreted in the framework of the gauge theory formulation of quantum mechanics which was proposed recently. An intriguing analogy is found between the lattice fermion problem (species doubling) and the problem of quantization in general.

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