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Dyson-Schwinger Equations in the Gribov Region

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On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions

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Abstract

In Chap. 2 I explained how to fix the gauge according to the conventional Faddeev-Popov procedure and that for non-perturbative calculations this is not sufficient due to the appearance of further gauge copies. Now I will go into the details of the improved gauge fixing suggested by Gribov and how this leads to a local Lagrangian amenable to the usual tools of quantum field theory. The resulting action is called Gribov-Zwanziger action and constitutes the best option available so far to achieve a complete gauge fixing within the path integral. For lattice simulations the situation is slightly different and I will comment on this in more detail in Sect. 6.1.3. Of course the ultimate goal would be a complete gauge fixing as, for example, provided by restriction to the fundamental modular region. This, however, does not seem realizable directly within the path integral due to the non-trivial topology of this region.

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Notes

  1. 1.

    The ghost fields \(c\) and \(\bar{c}\) have mass dimensions zero and two, respectively [11].

  2. 2.

    In Ref. [40] it is shown numerically that case III does not yield a solution and can be ruled out.

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  1. University of Graz, Graz, Austria

    Markus Q. Huber

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Huber, M.Q. (2012). Dyson-Schwinger Equations in the Gribov Region. In: On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27691-0_6

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