TRANSVERSAL AFFINE CONNECTION AND QUANTIZATION OF CONSTRAINED SYSTEMS

The Dirac quantization of a finite-dimensional relativistic system with a quadratic super-Hamiltonian and linear supermomenta is investigated. In a previous work, the operator constraints were consistently factor-ordered in such a way that the resulting quantum theory was invariant under all relevant transformations of the classical theory. The method was based on a special choice of coordinates and gauge. Here, coordinate-independent methods are worked out and a quite general gauge is used. A new mathematical concept, the so-called "transversal affine connection," is introduced. This connection is not a linear connection and is associated with a degenerate metric. The corresponding curvature tensor is defined and its components are calculated. The formalism is used to reconstruct the operator constraints, clarify their geometric meaning, and calculate their commutators. © 1990 American Institute of Physics.