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

@article{Pavi2001HowTG,
title={How the geometric calculus resolves the ordering ambiguity of quantum theory in curved space},
author={Matej Pav{\vs}i{\vc}},
journal={Classical and Quantum Gravity},
year={2001},
volume={20},
pages={2697-2714}
}
• M. Pavšič
• Published 27 November 2001
• Mathematics
• Classical and Quantum Gravity
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 ?? as p = ?i????. The product of two such operators is unambiguous, and such is the Hamiltonian which is just the d'Alembert operator in…
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## References

SHOWING 1-10 OF 98 REFERENCES

The automorphism invariant theory of Crawford[8] has shown great promise, however its application is limited by the paradigm to the domain of spin space. Our conjecture is that there is a broader
The relativistic quantum mechanics with Lorentz-invariant evolution parameter and indefinite mass is a very elegant theory. But it cannot be derived by quantizing the usual classical relativity in
An isomorphism is shown to exist between the group of point transformations in classical mechanics and a certain subgroup of the group of all unitary transformations in quantum mechanics. This
AbstractSchwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianLc( $$\dot x$$ , x)=(M/2)gij(x) $$\dot x$$ i $$\dot x$$
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These
A method known as covariant geodesic point separation is developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field. The
• Physics
• 1993
Multivector quantum mechanics utilizes wavefunctions which are Clifford aggregates (e.g. sum of scalar, vector, bivector). This is equivalent to multi- spinors constructed of Dirac matrices, with the
This paper is based on the elementary remark that the extraction of gauge invariant results from a formally gauge invariant theory is ensured if one employs methods of solution that involve only