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

Sergey Sergeev

    Research output: Contribution to journalArticle

    Abstract

    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)
    Original languageEnglish
    Pages (from-to)1-12
    Number of pages12
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume42
    Issue number29
    DOIs
    Publication statusPublished - 24 Jul 2009

    Fingerprint Dive into the research topics of 'Ground states of the Heisenberg evolution operator in discrete three-dimensional spacetime and quantum discrete BKP equations'. Together they form a unique fingerprint.

  • Cite this