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.. highlight:: c


.. _lattice_dyson_g_w:

lattice_dyson_g_w
=================

**Synopsis**:

.. code-block:: c

    triqs_tprf::g_w_t lattice_dyson_g_w (double mu, triqs_tprf::e_k_cvt e_k,
   triqs_tprf::g_w_cvt sigma_w)

Construct an interacting Matsubara frequency local (:math:`\mathbf{r}=\mathbf{0}`) lattice Green's function :math:`G_{a\bar{b}}(i\omega_n)`


Parameters
----------

 * **mu**: chemical potential :math:`\mu`

 * **e_k**: discretized lattice dispersion :math:`\epsilon_{\bar{a}b}(\mathbf{k})`

 * **sigma_w**: imaginary frequency self-energy :math:`\Sigma_{\bar{a}b}(i\omega_n)`



Return value
------------

Matsubara frequency lattice Green's function $G_{a\bar{b}}(i\omega_n, \mathbf{k})$

Documentation
-------------


 Computes

 .. math::
    G_{a\bar{b}}(i\omega_n) = \frac{1}{N_k} \sum_\mathbf{k} \left[
        (i\omega_n + \mu ) \cdot \mathbf{1}  - \epsilon(\mathbf{k}) - \Sigma(i\omega_n)
	\right]^{-1}_{a\bar{b}},

 using a discretized dispersion :math:`\epsilon_{\bar{a}b}(\mathbf{k})`,
 chemical potential :math:`\mu`, and a momentum independent Matsubara frequency
 self energy :math:`\Sigma_{\bar{a}b}(i\omega_n)`.