dorsal/arxiv
View SchemaSymmetries of the Poincare sphere and decoherence matrices
| Authors | S. Baskal, Y. S. Kim |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501050 |
| URL | https://arxiv.org/abs/quant-ph/0501050 |
Abstract
The Stokes parameters form a Minkowskian four-vector under various optical transformations. As a consequence, the resulting two-by-two density matrix constitutes a representation of the Lorentz group. The associated Poincare sphere is a geometric representation of the Lorentz group. Since the Lorentz group preserves the determinant of the density matrix, it cannot accommodate the decoherence process through the decaying off-diagonal elements of the density matrix, which yields to an incerese in the value of the determinant. It is noted that the O(3,2) deSitter group contains two Lorentz subgroups. The change in the determinant in one Lorentz group can be compensated by the other. It is thus possible to describe the decoherence process as a symmetry transformation in the O(3,2) space. It is shown also that these two coupled Lorentz groups can serve as a concrete example of Feynman's rest of the universe.
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"abstract": "The Stokes parameters form a Minkowskian four-vector under various optical\ntransformations. As a consequence, the resulting two-by-two density matrix\nconstitutes a representation of the Lorentz group. The associated Poincare\nsphere is a geometric representation of the Lorentz group. Since the Lorentz\ngroup preserves the determinant of the density matrix, it cannot accommodate\nthe decoherence process through the decaying off-diagonal elements of the\ndensity matrix, which yields to an incerese in the value of the determinant. It\nis noted that the O(3,2) deSitter group contains two Lorentz subgroups. The\nchange in the determinant in one Lorentz group can be compensated by the other.\nIt is thus possible to describe the decoherence process as a symmetry\ntransformation in the O(3,2) space. It is shown also that these two coupled\nLorentz groups can serve as a concrete example of Feynman\u0027s rest of the\nuniverse.",
"arxiv_id": "quant-ph/0501050",
"authors": [
"S. Baskal",
"Y. S. Kim"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Symmetries of the Poincare sphere and decoherence matrices",
"url": "https://arxiv.org/abs/quant-ph/0501050"
},
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