Pacific Journal of Mathematics

Tau functions for the Dirac operator in the Euclidean plane.

John Palmer

Article information

Source
Pacific J. Math., Volume 160, Number 2 (1993), 259-342.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102624217

Mathematical Reviews number (MathSciNet)
MR1233355

Zentralblatt MATH identifier
0777.35068

Subjects
Primary: 58F07
Secondary: 58G26 81T10: Model quantum field theories

Citation

Palmer, John. Tau functions for the Dirac operator in the Euclidean plane. Pacific J. Math. 160 (1993), no. 2, 259--342. https://projecteuclid.org/euclid.pjm/1102624217


Export citation

References

  • [1] E. Barouch, B. M. McCoy and T. T. Wu, Zero-fieldsusceptibility of the two- dimensional Ising model near Tc, Phys. Rev. Lett., 31 (1973), 1409-1411. C. A. Tracy and B. M. McCoy, Neutron scattering and the correlations of the Ising model near Tc, Phys. Rev. Lett., 31 (1973), 1500-1504.
  • [2] A. Carey, S. Ruijsennaars and J. Wright, The massless Thirring model: positivity ofKlaiber's N-point function, Comm. Math. Phys., 99 (1985), 347.
  • [3] R. Davey, SMJ analysis of monodromy fields, thesis, unpublished (University of Arizona 1988).
  • [4] B. Malgrange, Sur les deformations isomonodromiques, in Mathematique et Physique. Seminaire de Ecole Normale Superieure 1979-1982, L. B. deMon- vel, A. Douady, and J. L. Verdier, eds. (Birkhauser, Boston, 1983), 400-426.
  • [5] B. Malgrange, Deformations Isomonodromiques et Functions , extract of a letter to J. B. Bost, November 28, 1986.
  • [6] R. Narayanan and C. A. Tracy, Holonomic quantum field theory of Bosons in the Poincare disk and the zero curvature limit, Nuclear Phys., B340 (1990), 568-594.
  • [7] J. Palmer,Monodromy fields on Z2, Comm. Math. Phys., 102 (1985), 175-206.
  • [8] J. Palmer, Determinants of Cauchy-Riemann operators as functions, Acta Appl. Math., 18 No. 3 (1990), 199-223.
  • [9] J. Palmer and C. Tracy, Two dimensional Ising correlations: the SMJ analysis, Adv. in Appl. Math., 4 (1983), 46-102.
  • [10] J. Palmer and C. Tracy, Monodromy preserving deformations of the Dirac operator on the hyper- bolicplane, in Mathematicsof NonlinearScience: proceedings of an AMS spe- cial session held January 11-14, 1989, M. S. Berger ed., Contemp. Math., 108, 119-131.
  • [11] A. Pressley and G. Segal, Loop Groups,Clarendon Press, Oxford (1986).
  • [12] D. Quillen, Determinants of Cauchy-Riemann operatorson a Riemann surface, Functional Anal. Appl., 19 (1985), 37-41.
  • [13] S. N.M. Ruijsenaars, The Wightman axioms for thefermionic Federbush modeL Comm. Math. Phys., 87 (1982), 181-228.
  • [14] M. Sato, T. Miwa and M. Jimbo, Holonomic quantum fields I-V Publ. RIMS, Kyoto Univ., 14 (1978), 223-267, 15 (1979), 201-278, 15 (1979), 577-629, 15 (1979), 871-972, 16 (1980), 531-584.
  • [15] G. Segal and G. Wilson, Loop groups and equations of KdV type, Publ. Math. I.H.E.S., 61 (1985), 5-65.
  • [16] C. A. Tracy, Monodromy preserving deformation theory for theKlein-Gordon equation in the hyperbolicplane, Phys., 34D (1989), 347-365.
  • [17] C. A. Tracy, Monodromy preserving deformations of linear ordinary and partial differ- ential equations, in Solitons in Physics, Mathematics, and NonlinearOptics, P. J. Olver, and D. H. Sattinger (eds.), Springer-Verlag, New York, (1990), 165-174.
  • [18] E. Witten, Quantum field theory, Grassmannians and algebraiccurves, Comm. Math. Phys., 113 (1988), 529-600.
  • [19] T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch, Spin-spin correlation functions for the two dimensional Ising model: Exact theory in the scalingregion, Phys. Rev. B, 13 (1976), 316-374.
  • [20] B. M. McCoy, C. A. Tracy, and T. T. Wu, Painlevefunctions of the third kind, J. Math. Phys., 18 (1977), 1058-1092
  • [21] C. A. Tracy, symptotics of a -function arising in the two-dimensional Ising model, Comm. Math. Phys., 142 (1991), 297-311. E. L. Basor and C. A. Tracy, symptotics of a tau-function and Toeplitzdeter- minants with singular generating functions, Internat. J. Modern Physics A 7, Suppl. 1A(1992), 83-107.