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How the geometric calculus resolves the ordering ambiguity of quantum theory in curved space

2003
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Classical and quantum gravity
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The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum operator is defined to be the vector derivative (the gradient) multiplied by $-i$; it can be expanded in terms of basis vectors $\gamma_\mu$ as $p = -i \gamma^\mu \p_\mu$. The product of two such operators is unambiguous, and such is the Hamiltonian which is just

doi:10.1088/0264-9381/20/13/318
fatcat:laxcgg4vkjac3hsfi42nhw2fba