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Coulomb Confinement

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An Introduction to the Confinement Problem

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

Abstract

The Gribov horizon, Neuberger’s theorem, and the Gribov-Zwanziger confinement scenario. Coulomb confinement as a necessary condition for confinement. Numerical results for the Coulomb potential on the lattice, and the low-lying Faddeev-Popov eigenvalue spectrum. The role of center vortices in Coulomb confinement.

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Notes

  1. 1.

    BRST quantization is described in most modern textbooks on quantum field theory; e.g. [5].

  2. 2.

    At the quantum level, the Hamiltonian contains factors of \((\det M)^{1/2}\) and \((\det M)^{-1/2}\), which cancel out in the classical limit where the ordering of operators is irrelevant [8]. These factors also cancel out in the expression for the Coulomb energy due to static color sources.

  3. 3.

    Another approach is to calculate 〈K ab(x, y; A)〉 directly, via Monte Carlo simulations. This computationally more demanding procedure has been followed in [11] for the SU(3) gauge group, with the result that the Coulomb potential is linearly confining, with a string tension that is greater (by a factor estimated at 1.6) than the asymptotic string tension.

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Greensite, J. (2020). Coulomb Confinement. 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_10

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