triqs_ctseg::measure_gl
#include <triqs_ctseg.hpp>
class measure_gl
Measure for the Green’s function in Legendre basis
- The Legendre coefficients of the Green’s function and the improved estimator
are defined as
\[X(l)=\sqrt{2l+1}\int_0^\beta d\tau\,P_l[x(\tau)]X(\tau)\]
with \(X=G^\sigma_{ab},F^\sigma_{ab}\), \(x(\tau)=2\tau/\beta-1\) and \(P_l(x)\) are the Legendre polynomials, defined in the [-1,1] interval.
- These measurements are controlled through the switches and parameter
measure_gl,measure_flandn_legendre_g.- The Legendre Green’s function may be transformed to the Matsubara basis
through the unitary transformation
\(G_a(i\omega_n) = \sum_{l\geq 0}T_{nl} G_a(l)\)
where
\(T_{nl} = (-1)^ni^{l+1}\sqrt{2l+1}j_l\left(\frac{(2n+1)\pi}{2}\right)\)
with the spherical Bessel functions \(j_l(z)\).