Symplectic Dirac-Kähler Fields

Abstract

For the description of space-time fermions, Dirac-Kähler 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-Kähler 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-Kähler 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.

86 pages, latex

References in corpus (1)

• Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations

Cited by in corpus (6)

• Dirac-Kähler approach connected to quantum mechanics in Grassmann space
• Classification of 1st order symplectic spinor operators over contact projective geometries
• Howe type duality for metaplectic group acting on symplectic spinor valued forms
• On the chirality of a discrete Dirac-Kähler equation
• Complex of twistor operators in symplectic spin geometry
• Structure of the curvature tensor on symplectic spinors