The commutativity of quantized first- and higher-order Hamiltonians

K. Ikeda

doi:10.1088/0305-4470/27/17/028

The commutativity of quantized first- and higher-order Hamiltonians

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Abstract

The key point of the Hamiltonian formalism of Toda molecules is the commutativity of the Hamiltonians (tr y^k, tr y^l)=0, where y in GL(n) and (,) is a Poisson bracket associated with the classical r-matrix. To quantize the Toda molecule, we have to consider the q-analogue of the above formula. In this paper, we show the commutativity of the quantized first- and higher-order Hamiltonians (tr_q X^m, tr_q X)=0, where X is a matrix of quantum group GL_q(n).

Original language	English
Article number	028
Pages (from-to)	5969-5977
Number of pages	9
Journal	Journal of Physics A: Mathematical and General
Volume	27
Issue number	17
DOIs	https://doi.org/10.1088/0305-4470/27/17/028
Publication status	Published - 1994 Dec 1
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/27/17/028

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The commutativity of quantized first- and higher-order Hamiltonians

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