Branes, Quantum Nambu Brackets, and the Hydrogen Atom

TL;DR

This paper demonstrates how Nambu Bracket quantization can be applied to the Hydrogen atom, illustrating a general method that extends beyond traditional Hamiltonian quantization, with implications for topological open branes.

Contribution

It introduces a consistent quantization of Nambu Brackets for the Hydrogen atom, showing the method's applicability to superintegrable systems and topological branes.

Findings

Quantum Nambu Brackets form an associative structure.

The method reproduces known results for the Hydrogen atom.

Applicable to systems beyond Hamiltonian dynamics.

Abstract

The Nambu Bracket quantization of the Hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu Brackets. Such branes then may be quantized through the consistent quantization of the underlying Nambu brackets: properly defined, the Quantum Nambu Brackets comprise an associative structure, although the naive derivation property is mooted through operator entwinement. For superintegrable systems, such as the Hydrogen atom, the results coincide with those furnished by Hamiltonian quantization--but the method is not limited to Hamiltonian systems.