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  • 11
    Electronic Resource
    Electronic Resource
    The spectral problem for the q-Knizhnik-Zamolodchikov equation
    Amsterdam : Elsevier
    Physics Letters B 311 (1993), S. 103-109 
    Details
    ISSN: 0370-2693
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0370-2693(93)90541-O
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  • 12
    Electronic Resource
    Electronic Resource
    Unification of all string models with c〈1
    Amsterdam : Elsevier
    Physics Letters B 275 (1992), S. 311-314 
    Details
    ISSN: 0370-2693
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0370-2693(92)91595-Z
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  • 13
    Electronic Resource
    Electronic Resource
    Single-particle density matrix of a one-dimensional system of spin 1/2 Fermi particles (1990)
    Springer
    Theoretical and mathematical physics 85 (1990), S. 1321-1325 
    Details
    ISSN: 1573-9333
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01018409
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  • 14
    Electronic Resource
    Electronic Resource
    Conformal Maps and Integrable Hierarchies (2000)
    Springer
    Communications in mathematical physics 213 (2000), S. 523-538 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy singled out by the conditions known as “string equations”. The same hierarchy locally solves the 2D inverse potential problem, i.e., reconstruction of the domain out of a set of its harmonic moments. This is the same solution which is known to describe 2D gravity coupled to c= matter. We also introduce a concept of the τ-function for analytic curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200000249
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  • 15
    Electronic Resource
    Electronic Resource
    Non-archimedean strings and Bruhat-Tits trees (1989)
    Springer
    Communications in mathematical physics 123 (1989), S. 463-483 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the Bruhat-Tits tree for thep-adic linear groupGL(2) is a natural non-archimedean analog of the open string world sheet. The boundary of the tree can be identified with the field ofp-adic numbers. We construct a “lattice” quantum field theory on the Bruhat-Tits tree with a simple local lagrangian and show that it leads to the Freund-Olson amplitudes for emission processes of the particle states from the boundary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238811
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  • 16
    Electronic Resource
    Electronic Resource
    Multiloop calculations inp-adic string theory and Bruhat-Tits trees (1989)
    Springer
    Communications in mathematical physics 125 (1989), S. 675-711 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We treat the openp-adic string world sheet as a coset spaceF=T/Γ, whereT is the Bruhat-Tits tree for thep-adic linear groupGL(2, ℚ p ) and Γ⊂PGL(2, ℚ p ) is some Schottky group. The boundary of this world sheet corresponds to ap-adic Mumford curve of finite genus. The string dynamics is governed by the local gaussian action on the coset spaceF. The tachyon amplitudes expressed in terms ofp-adic θ-functions are proposed for the Mumford curve of arbitrary genus. We compare them with the corresponding usual archimedean amplitudes. The sum over moduli space of the algebraic curves is conjectured to be expressed in the arithmetic surface terms. We also give the necessary mathematical background including the Mumford approach top-adic algebraic curves. The connection of the problem of closedp-adic strings with the considered topics is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228348
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  • 17
    Electronic Resource
    Electronic Resource
    Quantum Integrable Models and Discrete Classical Hirota Equations (1997)
    Springer
    Communications in mathematical physics 188 (1997), S. 267-304 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: The standard objects of quantum integrable systems are identified with elements of classical nonlinear integrable difference equations. The functional relation for commuting quantum transfer matrices of quantum integrable models is shown to coincide with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice with open boundaries. Elliptic solutions of Hirota's equation give a complete set of eigenvalues of the quantum transfer matrices. Eigenvalues of Baxter's Q-operator are solutions to the auxiliary linear problems for classical Hirota's equation. The elliptic solutions relevant to the Bethe ansatz are studied. The nested Bethe ansatz equations for A k-1 -type models appear as discrete time equations of motions for zeros of classical τ-functions and Baker-Akhiezer functions. Determinant representations of the general solution to bilinear discrete Hirota's equation are analysed and a new determinant formula for eigenvalues of the quantum transfer matrices is obtained. Difference equations for eigenvalues of the Q-operators which generalize Baxter's three-term T−Q-relation are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050165
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  • 18
    Electronic Resource
    Electronic Resource
    Elliptic Solutions to Difference Non-Linear Equations and Related Many-Body Problems (1998)
    Springer
    Communications in mathematical physics 193 (1998), S. 373-396 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We study algebro-geometric (finite-gap) and elliptic solutions of fully discretized KP or 2D Toda equations. In bilinear form they are Hirota's difference equation for τ-functions. Starting from a given algebraic curve, we express the τ-function and the Baker–Akhiezer function in terms of the Riemann theta function. We show that the elliptic solutions, when the τ-function is an elliptic polynomial, form a subclass of the general algebro-geometric solutions. We construct the algebraic curves of the elliptic solutions. The evolution of zeros of the elliptic solutions is governed by the discrete time generalization of the Ruijsenaars-Schneider many body system. The zeros obey equations which have the form of nested Bethe-ansatz equations, known from integrable quantum field theories. We discuss the Lax representation and the action-angle-type variables for the many body system. We also discuss elliptic solutions to discrete analogues of KdV, sine-Gordon and 1D Toda equations and describe the loci of the zeros.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050333
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