On the ground state of Yang–Mills theory (original) (raw)
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Is the ground state of Yang-Mills theory Coulombic?
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We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit. * theinzl@plymouth.ac.uk
Probing the ground state in gauge theories
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We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string description is better in the confined phase but the Coulombic description is best in the deconfined phase; the last result is shown to agree with analytical calculations. Surprisingly in the non-abelian theory the Coulombic description is better in both the Higgs and confined phases. This indicates a significant difference in the width of the flux tubes in the two theories.
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We show how SU(3)C chromodynamics, which is the theory of strong interactions, is a corollary theory emerging naturally from the combination of nothing other than Maxwell / Weyl gauge theory with Yang-Mills theory. In the process, we show not only the emergence from the Maxwell / Yang-Mills combination of all that is to be expected from SU(3)C chromodynamics, but additionally, we show how the observed baryons containing three colored quarks in the ground state are the magnetic charges of Yang-Mills gauge theory and how these magnetic charges naturally confine their quarks and gluons but do pass mesons in order to interact. That is, we explain quark and gluon confinement and how it is that strong interactions are mediated by mesons but not gauge fields. Additionally, we demonstrate how the inherent non-linearity of Yang-Mills theory may be used to solve the “mass gap” problem and yield a nuclear interaction that is short range notwithstanding its being based on massless gluon gauge f...
Low-energy effective Yang-Mills theory for quark and gluon confinement
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We derive a gauge-invariant low-energy effective model of the Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type and agrees with it when a mass term which breaks nilpotency of the BRST symmetry is included. We show that the effective model with gluon propagator of the Gribov-Stingl type exhibits both quark and gluon confinement: the Wilson loop average has the area law and the Schwinger function violates reflection positivity. However, we argue that both quark and gluon confinement can be obtained even in the absence of such a mass term.