QUANTUM BI-HAMILTONIAN SYSTEMS-Reference-Cited by-同舟云学术

QUANTUM BI-HAMILTONIAN SYSTEMS

Published:2000-12-10 Issue:30 Volume:15 Page:4797-4810
ISSN:0217-751X
Container-title:International Journal of Modern Physics A
language:en
Short-container-title:Int. J. Mod. Phys. A

Author:

CARIÑENA JOSÉ F.¹,GRABOWSKI JANUSZ²³,MARMO GIUSEPPE⁴

Affiliation:

1. Depto. Física Teórica, Univ. de Zaragoza, 50009 Zaragoza, Spain

2. Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland

3. Mathematical Institute, Polish Academy of Sciences, ul. Śniadeckich 8, P.O. Box 137, 00-905 Warszawa, Poland

4. Dipartimento di Scienze Fisiche, Università Federico II di Napoli and INFN, Sezione di Napoli, Complesso Universitario di Monte Sant'Angelo, Via Cintia, 80125 Napoli, Italy

Abstract

We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217751X00001956

Reference9 articles.

1. A simple model of the integrable Hamiltonian equation

2. Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?

3. Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics

4. Wigner’s problem for a precessing magnetic dipole

5. On the Cohomology Theory for Associative Algebras

Cited by 71 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Generalized NS-algebras;Journal of Pure and Applied Algebra;2025-01

2. Curved -operator systems;Communications in Algebra;2024-07-14

3. Nijenhuis operators and associative D-bialgebras;Journal of Algebra;2024-02

4. Compatible Structures of Nonsymmetric Operads, Manin Products and Koszul Duality;Applied Categorical Structures;2024-01-10

5. Some algebraic structures about Nijenhuis operators;FILOMAT;2024