dorsal/arxiv
View SchemaA Possible Generalization of Quantum Mechanics
| Authors | Yu Tian |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512127 |
| URL | https://arxiv.org/abs/quant-ph/0512127 |
Abstract
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes values in the corresponding group algebra. This formalism admits a probability interpretation and a suitable dynamics, but has no obvious classical correspondence. Allowing the Lagrangian or the action functional to take values in a general Lie algebra instead of only the real number field (actually the u(1) algebra) enlarges the extent of possible physical laws that can describe the real world. The generalized quantum dynamics of a point particle in a background gauge field is given as an example, which realizes the gauge invariance by a Wilson line structure and shows that some Schrodinger-like equation can be deduced within this formalism. Some possible developments of this formalism are also discussed.
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"abstract": "A \"minimal\" generalization of Quantum Mechanics is proposed, where the\nLagrangian or the action functional is a mapping from the (classical) states of\na system to the Lie algebra of a general compact Lie group, and the wave\nfunction takes values in the corresponding group algebra. This formalism admits\na probability interpretation and a suitable dynamics, but has no obvious\nclassical correspondence. Allowing the Lagrangian or the action functional to\ntake values in a general Lie algebra instead of only the real number field\n(actually the u(1) algebra) enlarges the extent of possible physical laws that\ncan describe the real world. The generalized quantum dynamics of a point\nparticle in a background gauge field is given as an example, which realizes the\ngauge invariance by a Wilson line structure and shows that some\nSchrodinger-like equation can be deduced within this formalism. Some possible\ndevelopments of this formalism are also discussed.",
"arxiv_id": "quant-ph/0512127",
"authors": [
"Yu Tian"
],
"categories": [
"quant-ph"
],
"title": "A Possible Generalization of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0512127"
},
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