Korepin, V. E. Calculation of norms of Bethe wave functions. (English) Zbl 0531.60096 Commun. Math. Phys. 86, 391-418 (1982). The Bethe approach has been used successfully to solve many two dimensional models in quantum statistical mechanics. Recently these solutions have been investigated using the newly developed method of quantum inverse scattering (for systems in a finite box) yielding the results that the norms of these eigenfunctions of the Hamiltonian are equal to some Jacobians [see M. Gaudin, B. M. McCoy, and T. T. Wu, Normalization sum for the Bethe’s hypothesis wave functions of the Heisenberg-Ising chain. Phys. Rev. D 23, 417-419 (1981)]. The author has supplied the proof of this conjecture for a class of models. The main corpus of the paper consists of a generalization of this to cover a six vertex model necessitating the consideration of an inhomogeneous monodromy matrix. Some models like the quantum nonlinear Schrödinger equation are also treated as illustrations. Reviewer: Y.Prahalad Cited in 1 ReviewCited in 300 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B10 Quantum equilibrium statistical mechanics (general) 82B26 Phase transitions (general) in equilibrium statistical mechanics Keywords:inverse scattering method; monodromy matrix; Normalization; Schrödinger equation PDFBibTeX XMLCite \textit{V. E. Korepin}, Commun. Math. Phys. 86, 391--418 (1982; Zbl 0531.60096) Full Text: DOI References: [1] Bethe, H.: Z. Phys.71, 205-226 (1931) · doi:10.1007/BF01341708 [2] Yang, C.N., Yang, C.P.: Phys. Rev.150, 321-327 (1966) · doi:10.1103/PhysRev.150.321 [3] Lieb, E.H.: Phys. Rev. Lett.18, 692-694 (1967) · doi:10.1103/PhysRevLett.18.692 [4] Berezin, F.A., Pokhil, C.P., Finkelberg, V.M.: Vestn. Mosk. Gos. Univ. Ser.1.1, 21-28 (1964) [5] McGuire, J.B.: J. Math. Phys.5, 622-636 (1964); · Zbl 0131.43804 · doi:10.1063/1.1704156 [6] Brézin, E., Zinn-Justin, J.: C.R. Acad. Sci. Paris263, 670-673 (1966); [7] Gaudin, M.: J. Math. Phys.12, 1674-1676, 1677-1680 (1971) · doi:10.1063/1.1665790 [8] Faddeev, L.D.: Sov. Sci. Rev. Math. Phys. C1, 107-160 (1981) [9] Faddeev, L.D., Takhtajan, L.A.: Usp. Mat. Nauk34, 13-63 (1979) [10] Gaudin, M.: Preprint, Centre d’Etudes Nucleaires de Saclay, CEA-N-1559, (1), (1972) [11] Gaudin, M., McCoy, B.M., Wu, T.T.: Phys. Rev. D23, 417-419 (1981) [12] Baxter, R.J.: J. Stat. Phys.9, 145-182 (1973) · doi:10.1007/BF01016845 [13] Izergin, A.G., Korepin, V.E.: Lett. Math. Phys. (to be published) [14] Faddeev, L.D., Sklyanin, E.K.: Dokl. Akad. Nauk SSSR243, 1430-1433 (1978) [15] Sklyanin, E.K.: Dokl. Akad. Nauk SSSR244, 1337-1341 (1978) [16] Izergin, A.G., Korepin, V.E., Smirnov, F.A.: Teor. Mat. Fiz.48, 319-323 (1981) [17] Sklyanin, E.K.: Zap. Nauchn. Seminarov LOMI95, 55-128 (1980) [18] Izergin, A.G., Korepin, V.E.: Dokl. Akad. Nauk SSSR259, 76-79 (1981) [19] Izergin, A.G., Korepin, V.E.: Nucl. Phys. B, Field Theory and Statistical Systems B205 [FS5], 401-413 (1982) · doi:10.1016/0550-3213(82)90365-0 [20] Izergin, A.G., Korepin, V.E.: Lett. Math. Phys.5, 199-205 (1981) · doi:10.1007/BF00420699 [21] Baxter, R.J.: Stud. Appl. Math.L50, 51-67 (1971) [22] Belavin, A.A.: Phys. Lett. B87, 117-121 (1980) [23] Kulish, P.P.: Physica D3, 246-257 (1981) [24] Faddeev, L.D., Takhtajan, L.A.: Zap. Nauchn. Seminarov LOMI109, 134-178 (1981) [25] Baxter, R.J.: Philos. Trans. Soc. London, Ser. A289, 315-346 (1978) · doi:10.1098/rsta.1978.0062 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.