dorsal/arxiv
View SchemaDual Algebraic Pairs and Polynomial Lie Algebras in Quantum Physics: Foundations and Geometric Aspects
| Authors | V. P. Karassiov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304118 |
| URL | https://arxiv.org/abs/quant-ph/0304118 |
Abstract
We discuss some aspects and examples of applications of dual algebraic pairs $({\cal G}_1,{\cal G}_2)$ in quantum many-body physics. They arise in models whose Hamiltonians $H$ have invariance groups $G_i$. Then one can take ${\cal G}_1 = G_i$ whereas another dual partner ${\cal G}_2= g^D$ is generated by $G_i$ invariants, possesses a Lie-algebraic structure and describes dynamic symmetry of models; herewith polynomial Lie algebras $\hat g = g^D$ appear in models with essentially nonlinear Hamiltonians. Such an approach leads to a geometrization of model kinematics and dynamics.
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"abstract": "We discuss some aspects and examples of applications of dual algebraic pairs\n$({\\cal G}_1,{\\cal G}_2)$ in quantum many-body physics. They arise in models\nwhose Hamiltonians $H$ have invariance groups $G_i$. Then one can take ${\\cal\nG}_1 = G_i$ whereas another dual partner ${\\cal G}_2= g^D$ is generated by\n$G_i$ invariants, possesses a Lie-algebraic structure and describes dynamic\nsymmetry of models; herewith polynomial Lie algebras $\\hat g = g^D$ appear in\nmodels with essentially nonlinear Hamiltonians. Such an approach leads to a\ngeometrization of model kinematics and dynamics.",
"arxiv_id": "quant-ph/0304118",
"authors": [
"V. P. Karassiov"
],
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"quant-ph"
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"title": "Dual Algebraic Pairs and Polynomial Lie Algebras in Quantum Physics: Foundations and Geometric Aspects",
"url": "https://arxiv.org/abs/quant-ph/0304118"
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