Editing Path integral formulation (section)

=== Ordering prescription ===

Regardless of whether one works in configuration space or phase space, when equating the [[Mathematical formulation of quantum mechanics|operator formalism]] and the path integral formulation, an ordering prescription is required to resolve the ambiguity in the correspondence between non-commutative operators and the commutative functions that appear in path integrands.  For example, the operator <math>\frac{1}{2}(\hat{q}\hat{p}+\hat{p}\hat{q})</math> can be translated back as either <math>qp-\frac{i\hbar}{2}</math>, <math>qp+\frac{i\hbar}{2}</math>, or <math>qp</math> depending on whether one chooses the <math>\hat{q}\hat{p}</math>, <math>\hat{p}\hat{q}</math>, or Weyl ordering prescription; conversely, <math>qp</math> can be translated to either <math>\hat{q}\hat{p}</math>, <math>\hat{p}\hat{q}</math>, or <math>\frac{1}{2}(\hat{q}\hat{p}+\hat{p}\hat{q})</math> for the same respective choice of ordering prescription.