# Branes, Quantum Nambu Brackets and the Hydrogen Atom

@article{Zachos2004BranesQN, title={Branes, Quantum Nambu Brackets and the Hydrogen Atom}, author={C. Zachos and Thomas L. Curtright}, journal={Czechoslovak Journal of Physics}, year={2004}, volume={54}, pages={1393-1398} }

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…

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## References

SHOWING 1-10 OF 17 REFERENCES

### BRANES, STRINGS, AND ODD QUANTUM NAMBU BRACKETS

- Physics
- 2003

The dynamics of topological open branes is controlled by Nambu Brackets. Thus, they might be quantized through the consistent quantization of the underlying Nambu brackets, including odd ones: these…

### Phys Rev D68 (2003) 085001

- [hep-th/0212267]; also see New J Phys 4
- 2002

### 336-363; for an outstanding modern review, see G Valent

- Z Phys Am J Phys
- 1926

### Am J Phys

- Am J Phys
- 1976

### Odd-QNBs may be defined consistently through even ones of higher rank

### Phys Rev D68 (2003) 085001, [hep-th/0212267]; also see

- New J Phys
- 2002

### This clearly satisfies the Jacobi identity, but it fails a naive derivation property, as

- As a formal wisecrack, consider defining the following antisymmetric bracket

### Phys Rev 8 (1973) 2740-2743; F Lund and T Regge

- Phys Rev D14 (1976) 1524-1535; L Takhtajan, Commun Math Phys 160 (1994) 295-316; J Hoppe, Helv Phys Acta 70 (1997) 302-317, [hep-th/9602020]; Y Matsuo and Y Shibusa, JHEP02 (2001) 006, [hep-th/0010040]; B Pioline, Phys Rev D66 (2002) 025010; A De Castro et al., Phys Lett B584 (2004) 171-177, [hep-th
- 2004

### Phys Lett A285 (2001) 301-306; Y Nutku

- J Phys A36 (2003) 7559-7567, [quant-ph/0306059]. 2) Odd-QNBs may be defined consistently through even ones of higher rank. 3) As a formal wisecrack, consider defining the following antisymmetric bracket for a fixed operator 0, [[A,B]] ≡ AOB − BOA. This clearly satisfies the Jacobi identity, but it f
- 2004

### Int J Mod Phys A19

- Int J Mod Phys A19
- 2004