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Topological Quantum Computing Quantum Simulation

Quantum Torus symmetry of the KP, KdV and BKP hierarchies

arXiv
Authors: Chuanzhong Li, Jingsong He

Year

2013

Paper ID

31621

Status

Preprint

Abstract Read

~2 min

Abstract Words

114

Citations

N/A

Abstract

In this paper, we construct the quantum Torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy. That means we give a nice representation of the quantum Torus Lie algebra in the KP system by acting on its tau function. Comparing to the Winfty symmetry, this quantum Torus symmetry has a nice algebraic structure with double indices. Further by reduction, we also construct the quantum Torus symmetries of the KdV and BKP hierarchies and further derive the quantum Torus constraints on their tau functions. These quantum Torus constraints might have applications in the quantum field theory, supersymmetric gauge theory and so on.

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  • In this paper, we construct the quantum Torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1312.0758 [2] arXiv https://arxiv.org/abs/1312.0758 [3] Publisher https://arxiv.org/abs/1312.0758

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