On the noncommutative Feynman problem. (English) Zbl 1480.81076
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 22nd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 8–13, 2020. Sofia: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering. Geom. Integrability Quantization 22, 35-42 (2021).
Summary: We extend the Feynman derivation of the Maxwell-Lorentz equations to the case in which coordinates do not commute, adding significantly to previous results. New dynamics is pinned down precisely both at the level of the homogeneous equations and for the Lorentz force, for which a complete derivation is given for the first time.
For the entire collection see [Zbl 1468.53002].
For the entire collection see [Zbl 1468.53002].
MSC:
| 81R60 | Noncommutative geometry in quantum theory |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 78A25 | Electromagnetic theory (general) |
References:
| [1] | Acatrinei C., Lagrangian versus Quantization, J. Phys. A 37 (2004) 1225-1230. · Zbl 1046.81058 |
| [2] | Acatrinei C., A Simple Signal of Noncommutative Space, Mod. Phys. Lett. A 20 (2005) 1437-1442. · Zbl 1158.70308 |
| [3] | Acatrinei C., A Path Integral Leading to Higher-Order Lagrangians, J. Phys. A 40 (2007) F929-F934. · Zbl 1124.81029 |
| [4] | Acatrinei C., Comments on Noncommutative Particle Dynamics, Rom. J. Phys. 52 (2007) 3-13. · Zbl 1238.70011 |
| [5] | Acatrinei C., Dimensional Reduction for Generalized Poisson Brackets, J. Math. Phys. 49 (2008) 022903. · Zbl 1153.81303 |
| [6] | Acatrinei C., On the Feynman Problem in Noncommutative Space, submitted. · Zbl 1187.81198 |
| [7] | Boulahoual A. and Sedra M., Noncommutative Geometry Framework and the Feyn-man Proof of Maxwell Equations, J. Math. Phys. 44 (2003) 5888-5901. · Zbl 1063.81071 |
| [8] | Cariñena J. and Figueroa H., Feynman Problem in the Noncommutative Case, J. Phys. A 39 (2006) 3763-3769. · Zbl 1089.81042 |
| [9] | Cariñena J., Ibort L., Marmo G. and Stern A., The Feynman Problem and the Inverse Problem for Poisson Dynamics, Phys. Rep. 263 (1995) 153-212. |
| [10] | Dyson F., On Feynman’s Proof of the Maxwell Equations, Am. J. Phys. 58 (1990) 209-211. · Zbl 1142.78302 |
| [11] | Farquhar I., Comment on The Feynman-Dyson Proof of the Gauge Field Equations, Phys. Lett. A 151 (1990) 203-204. |
| [12] | Hojman S. and Shepley L., No Lagrangian? No Quantization!, J. Math. Phys. 32 (1991) 142-146. · Zbl 0850.70193 |
| [13] | Hughes R., On Feynman’s Proof of the Maxwell Equations, Am. J. Phys. 60 (1992) 301-306. |
| [14] | Jauch J., Gauge Invariance as a Consequence of Galilei Invariance, Helv. Phys. Acta 37 (1964) 284-292. · Zbl 0151.43805 |
| [15] | Lee C., The Feynman-Dyson Proof of the Gauge Field Equations, Phys. Lett. A 148 (1990) 146-148. |
| [16] | Tanimura S., Relativistic Generalization and Extension to the Non-Abelian Gauge Theory of Feynman’s Proof of the Maxwell Equations, Ann. Phys. 220 (1992) 229-247. · Zbl 0767.53062 |
| [17] | Vaidya A. and Farina C., Can Galilean Mechanics and Full Maxwell Equations Co-exist Peacefully?, Phys. Lett. A 153 (1991) 265-267. |
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