..
   Generated automatically by cpp2rst

.. highlight:: c
.. role:: red
.. role:: green
.. role:: param


.. _triqs_tprf__lattice_dyson_g_wk:

triqs_tprf::lattice_dyson_g_wk
==============================

*#include <triqs_tprf.hpp>*



**Synopsis**

 .. rst-class:: cppsynopsis

    1. | g_wk_t :red:`lattice_dyson_g_wk` (double :param:`mu`, e_k_cvt :param:`e_k`, g_w_cvt :param:`sigma_w`)

    2. | g_wk_t :red:`lattice_dyson_g_wk` (double :param:`mu`, e_k_cvt :param:`e_k`, g_wk_cvt :param:`sigma_wk`)

    3. | g_Dwk_t :red:`lattice_dyson_g_wk` (double :param:`mu`, e_k_cvt :param:`e_k`, g_Dwk_cvt :param:`sigma_wk`)

    4. | g_wk_t :red:`lattice_dyson_g_wk` (double :param:`mu`, e_k_cvt :param:`e_k`, g_w_cvt :param:`sigma_w`)

    5. | g_Dwk_t :red:`lattice_dyson_g_wk` (double :param:`mu`, e_k_cvt :param:`e_k`, g_Dw_cvt :param:`sigma_w`)

Documentation



 **1)**   Construct an interacting Matsubara frequency lattice Green's function :math:`G_{a\bar{b}}(i\omega_n, \mathbf{k})`

        Computes

        .. math::
           G_{a\bar{b}}(i\omega_n, \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)`.



 **2)**   Construct an interacting Matsubara frequency lattice Green's function :math:`G_{a\bar{b}}(i\omega_n, \mathbf{k})`

        Computes

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

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



 **3)**   Construct an interacting Matsubara frequency lattice Green's function :math:`G_{a\bar{b}}(i\omega_n, \mathbf{k})`

        Computes

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

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



 **4)**   Construct an interacting Matsubara frequency lattice Green's function :math:`G_{a\bar{b}}(i\omega_n, \mathbf{k})`

        Computes

        .. math::
           G_{a\bar{b}}(i\omega_n, \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)`.



 **5)**   Construct an interacting Matsubara frequency lattice Green's function :math:`G_{a\bar{b}}(i\omega_n, \mathbf{k})`

        Computes

        .. math::
           G_{a\bar{b}}(i\omega_n, \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 Matsubara frequency
        self energy :math:`\Sigma_{\bar{a}b}(i\omega_n)`.





Parameters
^^^^^^^^^^

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

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

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

 * :param:`sigma_wk` imaginary frequency self-energy :math:`\Sigma_{\bar{a}b}(i\omega_n, \mathbf{k})`


Returns
^^^^^^^

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