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

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

2004-06-13

arxiv.org/abs/gr-qc/0406054v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages

Scientific paper

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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