Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2001-09-10
Commun. Math. Phys. 216, 59-83 (2001)
Physics
Condensed Matter
Strongly Correlated Electrons
23 pages, 2 figures
Scientific paper
10.1007/s002200000324
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.
Cuniberti Gianaurelio
Micheli Enrico de
Viano Giovanni Alberto
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