Gluon propagator in an external field; what happens when the field is removed?

Axel Maas, Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    We exhibit some general bounds on the free energy W(J) in an SU(N) gauge theory, where Jb μ is a source for the gluon field Ab μ in the minimal Landau gauge, and W(J) is the generating functional of connected correlators, expW(J) = (exp(J,A)). We then specialize to a source J(x) = hcos(k-x) of definite momentum k and source strength h, and study the gluon propagator D(k,h) in the presence of this source. Among other relations, we prove f 0 dh D(k,h) ≤ V2k, which implies limk→0 D(k, h) = 0, for all positive h>0. This means that the system does not respond to a static color probe, no matter how strong. We also present numerical evaluations of the free energy W(k, h) and the gluon propagator D(k, h) for the case of SU(2) Yang-Mills theory in dimensions 2, 3 and 4 which are consistent with these findings, and we compare with recent lattice calculations at h = 0 which indicate that the gluon propagator in the minimum Landau gauge is finite, limk→0 D(k, 0) > 0. These lattice data together with our analytic results imply a jump in the value of D(k, h) at h = 0 and k = 0, and the value of D(k, h) at this point depends on the order of limits.

    Original languageEnglish (US)
    Article number047
    JournalUnknown Journal
    Volume02-06-September-2013
    StatePublished - Feb 12 2014

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    Propagator
    External Field
    Gages
    Free energy
    Free Energy
    Gauge
    Correlators
    Imply
    Momentum
    Correlator
    Yang-Mills Theory
    Gauge Theory
    Color
    Jump
    Probe
    Evaluation

    ASJC Scopus subject areas

    • General

    Cite this

    Maas, A., & Zwanziger, D. (2014). Gluon propagator in an external field; what happens when the field is removed? Unknown Journal, 02-06-September-2013, [047].

    Gluon propagator in an external field; what happens when the field is removed? / Maas, Axel; Zwanziger, Daniel.

    In: Unknown Journal, Vol. 02-06-September-2013, 047, 12.02.2014.

    Research output: Contribution to journalArticle

    Maas, A & Zwanziger, D 2014, 'Gluon propagator in an external field; what happens when the field is removed?', Unknown Journal, vol. 02-06-September-2013, 047.
    Maas A, Zwanziger D. Gluon propagator in an external field; what happens when the field is removed? Unknown Journal. 2014 Feb 12;02-06-September-2013. 047.
    Maas, Axel ; Zwanziger, Daniel. / Gluon propagator in an external field; what happens when the field is removed?. In: Unknown Journal. 2014 ; Vol. 02-06-September-2013.
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