.. _sphx_glr_auto_examples_Solid_State_Physics_plot_Gamma.py:


The Gamma function
==================

A diagram containing operators of various orders.




.. image:: /auto_examples/Solid_State_Physics/images/sphx_glr_plot_Gamma_001.png
    :align: center





.. code-block:: python

    import numpy as np
    import matplotlib.pyplot as plt
    from feynman import Diagram

    # Set up the figure and ax
    fig = plt.figure(figsize=(9,3))
    ax = fig.add_axes([0,0,1,1], frameon=False)

    ax.set_xlim(0, 3)
    ax.set_ylim(0, 1)

    y0 = sum(ax.get_ylim())/2.

    side = 0.3
    gammalen = side * np.sqrt(3) / 2
    linlen = 0.3
    txtpad = 0.2
    tail_marker = 'o'

    W_style = dict(style = 'double wiggly', nwiggles=2)
    v_style = dict(style = 'simple wiggly', nwiggles=2)
    G_style = dict(style = 'double',  arrow=True, arrow_param={'width':0.05})

    D = Diagram(ax)

    # Left hand size
    xy = [0.4, y0]
    v11 = D.vertex(xy, dy= side/2)
    v12 = D.vertex(xy, dy=-side/2)
    v13 = D.vertex(xy, dx=gammalen)
    gamma0 = D.operator([v11,v12,v13])
    gamma0.text("$\Gamma$")

    # Symbol
    D.text(v13.x + txtpad, y0, "=")

    # Create a three-vertex dot.
    chunkdist = .03
    chunklen = .03
    chunkstyle=dict(arrow=False, linewidth=6.)
    v20 = D.vertex([v13.x + 2 * txtpad, y0])
    v210 = D.vertex(v20.xy, angle=0.,   radius=chunkdist, marker='')
    v220 = D.vertex(v20.xy, angle=1./3, radius=chunkdist, marker='')
    v230 = D.vertex(v20.xy, angle=2./3, radius=chunkdist, marker='')
    v21  = D.vertex(v20.xy, angle=0.,   radius=chunkdist+chunklen, marker='')
    v22  = D.vertex(v20.xy, angle=1./3, radius=chunkdist+chunklen, marker='')
    v23  = D.vertex(v20.xy, angle=2./3, radius=chunkdist+chunklen, marker='')
    D.line(v210, v21, **chunkstyle)
    D.line(v220, v22, **chunkstyle)
    D.line(v230, v23, **chunkstyle)

    # Symbol
    D.text(v20.x + txtpad, y0, "+")

    # Second term
    xy = [v20.x + 2 * txtpad, y0]
    v31 = D.vertex(xy, dy= side/2)
    v32 = D.vertex(xy, dy=-side/2)
    v33 = D.vertex(xy, dy= side/2, dx=side)
    v34 = D.vertex(xy, dy=-side/2, dx=side)
    K = D.operator([v31,v32,v34,v33])
    K.text("$\\frac{\delta \Sigma}{\delta G}$")

    v41 = D.vertex(v33.xy, dx=linlen)
    v42 = D.vertex(v34.xy, dx=linlen)
    v43 = D.vertex((v41.xy+v42.xy)/2, dx=gammalen)

    G1 = D.line(v41, v33, **G_style)
    G2 = D.line(v34, v42, **G_style)

    gamma1 = D.operator([v41,v42,v43])
    gamma1.text("$\Gamma$")


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

**Total running time of the script:** ( 0 minutes  0.078 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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