Non-canonical Quantization of a Quadratic Constrained System

We propose an alternative to Dirac quantization for a quadratic constrained system. We show that this solves the Jacobi identity violation problem occuring in the Dirac quantization case and yields a well defined Fock space. By requiring the uniqueness of the ground state, we show that for non-constrained systems this approach gives the same results as Dirac quantization.