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

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    Evolution Operator
    Hilbert spaces
    Discrete Equations
    Ground state
    Ground State
    Mathematical operators
    eigenvectors
    Space-time
    operators
    Three-dimensional
    ground state
    R-matrix
    spectral theory
    Large Set
    Field Theory
    Discrete-time
    Hilbert space
    Subspace
    ingredients
    Eigenvalue

    Cite this

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    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)",
    author = "Sergey Sergeev",
    year = "2009",
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    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

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