dorsal/arxiv
View SchemaBuilding a frame and gauge free formulation of quantum mechanics
| Authors | T. Fulop, S. D. Katz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806067 |
| URL | https://arxiv.org/abs/quant-ph/9806067 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The wave function of quantum mechanics is not a boost invariant and gauge invariant quantity. Correspondingly, reference frame dependence and gauge dependence are inherited to most of the elements of the usual formulation of quantum mechanics (including operators, states and events). If a frame dependent and gauge dependent formalism is called, in short, a relative formalism, then the aim of the paper is to establish an absolute, i.e., frame and gauge free, reformulation of quantum mechanics. To fulfil this aim, we develop absolute quantities and the corresponding equations instead of the wave function and the Schr\"odinger equation. The absolute quantities have a more direct physical interpretation than the wave function has, and the corresponding equations express explicitly the independent physical aspects of the system which are contained in the Schr\"odinger equation in a mixed and more hidden form. Based on the absolute quantities and equations, events, states and physical quantities are introduced also in an absolute way. The formalism makes it possible to obtain some sharper versions of the uncertainty relation and to extend the validity of Ehrenfest's theorem. The absolute formulation allows wide extensions of quantum mechanics. To give examples, we discuss two known nonlinear extensions and, in close detail, a dissipative system. An argument is provided that the absolute formalism may lead to an explanation of the Aharonov-Bohm effect purely in terms of the electromagnetic field strength tensor. At last, on special relativistic and curved spacetimes, absolute quantities and equations instead of the Klein-Gordon wave function and equation are given, and their nonrelativistic limit is derived.
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"abstract": "The wave function of quantum mechanics is not a boost invariant and gauge\ninvariant quantity. Correspondingly, reference frame dependence and gauge\ndependence are inherited to most of the elements of the usual formulation of\nquantum mechanics (including operators, states and events). If a frame\ndependent and gauge dependent formalism is called, in short, a relative\nformalism, then the aim of the paper is to establish an absolute, i.e., frame\nand gauge free, reformulation of quantum mechanics. To fulfil this aim, we\ndevelop absolute quantities and the corresponding equations instead of the wave\nfunction and the Schr\\\"odinger equation. The absolute quantities have a more\ndirect physical interpretation than the wave function has, and the\ncorresponding equations express explicitly the independent physical aspects of\nthe system which are contained in the Schr\\\"odinger equation in a mixed and\nmore hidden form. Based on the absolute quantities and equations, events,\nstates and physical quantities are introduced also in an absolute way. The\nformalism makes it possible to obtain some sharper versions of the uncertainty\nrelation and to extend the validity of Ehrenfest\u0027s theorem. The absolute\nformulation allows wide extensions of quantum mechanics. To give examples, we\ndiscuss two known nonlinear extensions and, in close detail, a dissipative\nsystem. An argument is provided that the absolute formalism may lead to an\nexplanation of the Aharonov-Bohm effect purely in terms of the electromagnetic\nfield strength tensor. At last, on special relativistic and curved spacetimes,\nabsolute quantities and equations instead of the Klein-Gordon wave function and\nequation are given, and their nonrelativistic limit is derived.",
"arxiv_id": "quant-ph/9806067",
"authors": [
"T. Fulop",
"S. D. Katz"
],
"categories": [
"quant-ph",
"hep-th"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Building a frame and gauge free formulation of quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/9806067"
},
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