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Ghosts, Gluons, and Dyson-Schwinger Equations

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An Introduction to the Confinement Problem

Part of the book series: Lecture Notes in Physics ((LNP,volume 972))

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Abstract

Shortly after the recognition, in the 1970s, that the static quark potential ought to be linear with quark separation, there was an effort to show that the momentum space gluon propagator, in covariant gauges, goes as 1∕k 4 as k → 0. The reason this was considered desirable is that if we naively evaluate the static quark potential from one-gluon exchange, then it is not hard to show that a 1∕k 4 limit at low momenta leads to a linear potential. Attempts to derive this 1∕k 4 behavior were based on trying to solve a truncated set of Dyson-Schwinger equations (DSEs), but because of various ambiguities, and the doubtful validity of the truncation, the effort was abandoned after a few years.

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Notes

  1. 1.

    In a gauge theory quantized in Landau or Coulomb gauge, where the functional integration is restricted to the Gribov region, the integration does not result in a boundary term, because the Fadeev-Popov determinant vanishes on the boundary (i.e. on the Gribov horizon).

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Greensite, J. (2020). Ghosts, Gluons, and Dyson-Schwinger Equations. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 972. Springer, Cham. https://doi.org/10.1007/978-3-030-51563-8_11

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