.. _sphx_glr_auto_examples_Solid_State_Physics_plot_Dyson.py:


Dyson equation
==============

A dyson equation.




.. image:: /auto_examples/Solid_State_Physics/images/sphx_glr_plot_Dyson_001.png
    :align: center





.. code-block:: python

    import matplotlib.pyplot as plt
    from feynman import Diagram

    # Set up the figure and ax
    fig = plt.figure(figsize=(10,1.5))
    ax = fig.add_axes([.0,.0,1.,1.], frameon=False)

    ax.set_xlim(0, 1.0)
    ax.set_ylim(0, .15)

    l = 0.15  # Length of the propagator
    txt_l = 0.05  # Padding around the symbol
    op_l = 0.08  # Size of the operator

    G_style = dict(arrow=True, arrow_param={'width':0.02, 'length': 0.05}, style = 'double')
    G0_style = dict(arrow=True, arrow_param={'width':0.02, 'length': 0.05}, style = 'simple')
    text_prop = dict(y=0.02, fontsize=20)

    D = Diagram(ax)

    # Left hand side
    v11 = D.vertex(xy=[0.05, 0.06])
    v12 = D.vertex(v11.xy, dx=l)
    G = D.line(v11, v12, **G_style)
    G.text("$G$", **text_prop)

    # Symbol
    D.text(v12.x + txt_l, v12.y, "=")

    # First term
    v21 = D.vertex(v12.xy, dx=2*txt_l)
    v22 = D.vertex(v21.xy, dx=l)
    G0 = D.line(v21, v22, **G0_style)
    G0.text("$G_0$", **text_prop)

    # Symbol
    D.text(v22.x + txt_l, v22.y, "+")

    # Second term
    v31 = D.vertex(v22.xy, dx=2*txt_l)
    v32 = D.vertex(v31.xy, dx=l)
    v33 = D.vertex(v32.xy, dx=op_l)
    v34 = D.vertex(v33.xy, dx=l)
    D.line(v31, v32, **G0_style)
    D.line(v33, v34, **G_style)
    O = D.operator([v32,v33])
    O.text("$\Sigma$")

    # Plot and show
    D.plot()
    plt.show()

**Total running time of the script:** ( 0 minutes  0.060 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_Dyson.py <plot_Dyson.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_Dyson.ipynb <plot_Dyson.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_