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Zap. Nauchn. Sem. POMI, 1997, Volume 245, Pages 270–281 (Mi znsl545)  

This article is cited in 18 scientific papers (total in 18 papers)

On an identity for dual fields

N. A. Slavnov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The identity is derived which gives an opportunity to exclude auxilary quantum operators (“dual fields”) in formulas representing scalar products as determinants in some important particular cases. The identity is important for calculating correlation functions by means of the algebraic Bethe Ansatz.

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English version:
Journal of Mathematical Sciences (New York), 2000, 100:2, 2181–2188

Bibliographic databases:

UDC: 530.145+517.9
Received: 04.01.1997

Citation: N. A. Slavnov, “On an identity for dual fields”, Questions of quantum field theory and statistical physics. Part 14, Zap. Nauchn. Sem. POMI, 245, POMI, St. Petersburg, 1997, 270–281; J. Math. Sci. (New York), 100:2 (2000), 2181–2188

Citation in format AMSBIB
\by N.~A.~Slavnov
\paper On an identity for dual fields
\inbook Questions of quantum field theory and statistical physics. Part~14
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 245
\pages 270--281
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (New York)
\yr 2000
\vol 100
\issue 2
\pages 2181--2188

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    This publication is cited in the following articles:
    1. Korepin V.E., Slavnov N.A., “The determinant representation for quantum correlation functions of the sinh–Gordon model”, Journal of Physics A–Mathematical and General, 31:46 (1998), 9283–9295  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Oota T., “Two–point correlation functions in perturbed minimal models”, Journal of Physics A–Mathematical and General, 31:37 (1998), 7611–7625  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Korepin V.E., Oota T., “A determinant representation for a correlation function of the scaling Lee–Yang model”, Journal of Physics A–Mathematical and General, 31:19 (1998), L371–L380  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. A. I. Bugrij, V. N. Shadura, “Asymptotic expression for the correlation function of twisted fields in the two-dimensional Dirac model on a lattice”, Theoret. and Math. Phys., 121:2 (1999), 1535–1549  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. E. Korepin, N. A. Slavnov, “The Form Factors in a Finite Volume”, Proc. Steklov Inst. Math., 226 (1999), 72–85  mathnet  mathscinet  zmath
    6. Kitanine N., Maillet J.M., Terras V., “Form factors of the XXZ Heisenberg spin–1/2 finite chain”, Nuclear Physics B, 554:3 (1999), 647–678  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Kitanine N.A., Slavnov N.A., “The Algebraic Bethe Ansatz and the correlation functions of the Heisenberg magnet”, Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 35, 2001, 243–264  mathscinet  zmath  isi
    8. Kitanine N., Maillet J.M., Slavnov N.A., Terras V., “Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field”, Nuclear Physics B, 641:3 (2002), 487–518  crossref  mathscinet  zmath  isi  scopus  scopus
    9. N. A. Slavnov, “Integral Representations for Correlation Functions of the $XXZ$ Heisenberg Chain”, Theoret. and Math. Phys., 135:3 (2003), 828–835  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. N. A. Slavnov, “On Scalar Products in the Algebraic Bethe Ansatz”, Proc. Steklov Inst. Math., 251 (2005), 246–253  mathnet  mathscinet  zmath
    11. N. A. Slavnov, “The algebraic Bethe ansatz and quantum integrable systems”, Russian Math. Surveys, 62:4 (2007), 727–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Kitanine N., Kozlowski K., Maillet J.M., Slavnov N.A., Terras V., “On correlation functions of integrable models associated with the six–vertex R–matrix”, Journal of Statistical Mechanics–Theory and Experiment, 2007, P01022  crossref  mathscinet  isi  scopus  scopus
    13. Gritsev V., Rostunov T., Demler E., “Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas”, J Stat Mech Theory Exp, 2010, P05012  crossref  mathscinet  isi  elib  scopus  scopus
    14. N. A. Slavnov, “Vvedenie v teoriyu kvantovykh integriruemykh sistem. Kvantovoe nelineinoe uravnenie Shredingera”, Lekts. kursy NOTs, 18, MIAN, M., 2011, 3–118  mathnet  crossref  zmath  elib
    15. Wheeler M., “An Izergin-Korepin procedure for calculating scalar products in the six-vertex model”, Nuclear Phys B, 852:2 (2011), 468–507  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    16. Kitanine N., Kozlowski K.K., Maillet J.M., Slavnov N.A., Terras V., “The thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain”, J Stat Mech Theory Exp, 2011, P05028  crossref  isi  scopus  scopus
    17. Niccoli G., “Antiperiodic Spin-1/2 Xxz Quantum Chains by Separation of Variables: Complete Spectrum and Form Factors”, Nucl. Phys. B, 870:2 (2013), 397–420  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    18. Faldella S., Niccoli G., “Sov Approach For Integrable Quantum Models Associated With General Representations on Spin-1/2 Chains of the 8-Vertex Reflection Algebra”, J. Phys. A-Math. Theor., 47:11 (2014), 115202  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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