Reconstructing the Thermal Green Functionsat Real Times from Those at Imaginary Times
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 (nonperturbative) 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 imaginarytime correlator, the latter being taken at the discrete Matsubara imaginary energies, respectively in the upper and lower halfplanes. 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/s002200000324
 arXiv:
 arXiv:condmat/0109175
 Bibcode:
 2001CMaPh.216...59C
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Complex Variables;
 Mathematics  Mathematical Physics;
 Mathematics  Spectral Theory
 EPrint:
 23 pages, 2 figures