Communications in Mathematical Physics

, Volume 216, Issue 1, pp 59–83

Reconstructing the Thermal Green Functions¶at Real Times from Those at Imaginary Times

  • Giovanni Cuniberti
  • Enrico De Micheli
  • Giovanni Alberto Viano

Abstract:

By exploiting the analyticity and boundary value properties of the thermal Green functions that result from the KMS condition in both time and energy complex variables, we treat the general (non-perturbative) problem of recovering the thermal functions at real times from the corresponding functions at imaginary times, introduced as primary objects in the Matsubara formalism. The key property on which we rely is the fact that the Fourier transforms of the retarded and advanced functions in the energy variable have to be the “unique Carlsonian analytic interpolations” of the Fourier coefficients of the imaginary-time correlator, the latter being taken at the discrete Matsubara imaginary energies, respectively in the upper and lower half-planes. Starting from the Fourier coefficients regarded as “data set”, we then develop a method based on the Pollaczek polynomials for constructing explicitly their analytic interpolations.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Giovanni Cuniberti
    • 1
  • Enrico De Micheli
    • 2
  • Giovanni Alberto Viano
    • 3
  1. 1.Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.¶E-mail: cunibert@mpipks-dresden.mpg.deDE
  2. 2.Istituto di Cibernetica e Biofisica – Consiglio Nazionale delle Ricerche, Via De Marini 6, 16149 Genova, Italy. E-mail: demic@icb.ge.cnr.itIT
  3. 3.Dipartimento di Fisica – Università di Genova and Istituto Nazionale di Fisica Nucleare,¶Via Dodecaneso 33, 16146 Genova, Italy. E-mail: viano@ge.infn.itIT

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