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Quantum mechanics without spacetime IV : a noncommutative Hamilton-Jacobi equation

T. P. Singh
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Abstract

It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a noncommutative generalisation of the Hamilton-Jacobi equation. If a certain form for the metric in the noncommuting coordinate system is assumed, along with a correspondence rule for the commutation relations, it can be argued that this noncommutative Hamilton-Jacobi equation is equivalent to standard quantum mechanics.

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T. P. Singh. 2004-06-13. Quantum mechanics without spacetime IV : a noncommutative Hamilton-Jacobi equation. https://arxiv.org/abs/gr-qc/0406054

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