### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 29 |

DOIs | |

Publication status | Published - 24 Jul 2009 |

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**Ground states of the Heisenberg evolution operator in discrete three-dimensional spacetime and quantum discrete BKP equations.** / Sergeev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Ground states of the Heisenberg evolution operator in discrete three-dimensional spacetime and quantum discrete BKP equations

AU - Sergeev, Sergey

PY - 2009/7/24

Y1 - 2009/7/24

N2 - In this paper we consider three-dimensional quantum q-oscillator field theory without spectral parameters. We construct an essentially large set of eigenstates of evolution with unity eigenvalue of discrete time-evolution operator. All these eigenstates belong to a subspace of a total Hilbert space where an action of the evolution operator can be identified with quantized discrete BKP equations (synonym Miwa equations). The key ingredients of our construction are specific eigenstates of a single three-dimensional R-matrix. These eigenstates are boundary states for hidden three-dimensional structures of \mathscr{U}_q\big(B_n^{(1)}\big) and \mathscr{U}_q\big(D_n^{(1)}\big)

AB - In this paper we consider three-dimensional quantum q-oscillator field theory without spectral parameters. We construct an essentially large set of eigenstates of evolution with unity eigenvalue of discrete time-evolution operator. All these eigenstates belong to a subspace of a total Hilbert space where an action of the evolution operator can be identified with quantized discrete BKP equations (synonym Miwa equations). The key ingredients of our construction are specific eigenstates of a single three-dimensional R-matrix. These eigenstates are boundary states for hidden three-dimensional structures of \mathscr{U}_q\big(B_n^{(1)}\big) and \mathscr{U}_q\big(D_n^{(1)}\big)

U2 - 10.1088/1751-8113/42/29/295207

DO - 10.1088/1751-8113/42/29/295207

M3 - Article

VL - 42

SP - 1

EP - 12

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1751-8113

IS - 29

ER -