Limits...
Propagators and topology.

Maas A - Eur Phys J C Part Fields (2015)

Bottom Line: The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives.However, the mid-momentum behavior is significantly affected.These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.

View Article: PubMed Central - PubMed

Affiliation: Institute of Physics, University of Graz, Universitätsplatz 5, 8010 Graz, Austria.

ABSTRACT

Two popular perspectives on the non-perturbative domain of Yang-Mills theories are either in terms of the gluons themselves or in terms of collective gluonic excitations, i.e. topological excitations. If both views are correct, then they are only two different representations of the same underlying physics. One possibility to investigate this connection is by the determination of gluon correlation functions in topological background fields, as created by the smearing of lattice configurations. This is performed here for the minimal Landau gauge gluon propagator, ghost propagator, and running coupling, both in momentum and position space for SU(2) Yang-Mills theory. The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives. However, the mid-momentum behavior is significantly affected. These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.

No MeSH data available.


The gluon propagator (left panels) and dressing function (right panels) for different discretizations at fixed physical volume (1.7 fm) for different number of APE sweeps, being slightly smeared (top panels), moderately smeared (middle panels), or strongly smeared (bottom panels). Results are renormalized at 2 GeV
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Fig4: The gluon propagator (left panels) and dressing function (right panels) for different discretizations at fixed physical volume (1.7 fm) for different number of APE sweeps, being slightly smeared (top panels), moderately smeared (middle panels), or strongly smeared (bottom panels). Results are renormalized at 2 GeV

Mentions: The situation is somewhat different when the discretization is varied, as is visible in Fig. 4. While without smearing the ultraviolet part agrees within a few percent for these discretizations [49], already slightly smearing changes this. Then the ultraviolet tail is the stronger suppressed the coarser the discretization. This effect also increases with increasing number of APE sweeps. This is most visible at the renormalization point  GeV, where the dressing functions coincide without smearing, but differ after strong smearing. The effect is much less pronounced at small momenta. Thus the low-momentum regime is not overmuch affected by discretization effects, but the high-momentum tail is. This is not too surprising, since ultraviolet fluctuations are most affected by the smearing operation, and thus discretization effects should become more pronounced at large momenta.Fig. 4


Propagators and topology.

Maas A - Eur Phys J C Part Fields (2015)

The gluon propagator (left panels) and dressing function (right panels) for different discretizations at fixed physical volume (1.7 fm) for different number of APE sweeps, being slightly smeared (top panels), moderately smeared (middle panels), or strongly smeared (bottom panels). Results are renormalized at 2 GeV
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4376381&req=5

Fig4: The gluon propagator (left panels) and dressing function (right panels) for different discretizations at fixed physical volume (1.7 fm) for different number of APE sweeps, being slightly smeared (top panels), moderately smeared (middle panels), or strongly smeared (bottom panels). Results are renormalized at 2 GeV
Mentions: The situation is somewhat different when the discretization is varied, as is visible in Fig. 4. While without smearing the ultraviolet part agrees within a few percent for these discretizations [49], already slightly smearing changes this. Then the ultraviolet tail is the stronger suppressed the coarser the discretization. This effect also increases with increasing number of APE sweeps. This is most visible at the renormalization point  GeV, where the dressing functions coincide without smearing, but differ after strong smearing. The effect is much less pronounced at small momenta. Thus the low-momentum regime is not overmuch affected by discretization effects, but the high-momentum tail is. This is not too surprising, since ultraviolet fluctuations are most affected by the smearing operation, and thus discretization effects should become more pronounced at large momenta.Fig. 4

Bottom Line: The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives.However, the mid-momentum behavior is significantly affected.These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.

View Article: PubMed Central - PubMed

Affiliation: Institute of Physics, University of Graz, Universitätsplatz 5, 8010 Graz, Austria.

ABSTRACT

Two popular perspectives on the non-perturbative domain of Yang-Mills theories are either in terms of the gluons themselves or in terms of collective gluonic excitations, i.e. topological excitations. If both views are correct, then they are only two different representations of the same underlying physics. One possibility to investigate this connection is by the determination of gluon correlation functions in topological background fields, as created by the smearing of lattice configurations. This is performed here for the minimal Landau gauge gluon propagator, ghost propagator, and running coupling, both in momentum and position space for SU(2) Yang-Mills theory. The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives. However, the mid-momentum behavior is significantly affected. These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.

No MeSH data available.