Description of gluon propagation in the presence of anA2condensate

Abstract

There is a good deal of current interest in the condensate < A a µ A µ a > which has been seen to play an important role in calculations which make use of the operator product expansion.That development has led to the publication of a large number of papers which discuss how that condensate could play a role in a gauge-invariant formulation. In the present work we consider gluon propagation in the presence of such a condensate which we assume to be present in the vacuum. We show that the gluon propagator has no on-mass-shell pole and, therefore, a gluon cannot propagate over extended distances. That is, the gluon is a nonpropagating mode in the gluon condensate. In the present work we discuss the properties of both the Euclidean-space and Minkowski-space gluon propagator. In the case of the Euclidean-space propagator we can make contact with the results of QCD lattice calculations of the propagator in the Landau gauge. With an appropriate choice of normalization constants, we present a unified representation of the gluon propagator that describes both the Minkowski-space and Euclidean-space dynamics in which the < A a µ A µ a > condensate plays an important role.

Unified description of seagull cancellations and infrared finiteness of gluon propagators

“…Moreover, the inclusion of a small number of dynamical quarks ('unquenching') produces a relative suppression to the gluon propagator, but preserves the feature of saturation clearly intact [10]. Naturally, these results have attracted particular attention, since they offer a valuable opportunity to explore the nonperturbative dynamics of Yang-Mills theories, and even though some of the underlying ideas have a rather long history [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], various field-theoretic mechanisms that may account for this characteristic behavior have been considered in the more recent literature .…”

Non-Abelian vector backgrounds with restored Lorentz invariance

“…Apart from appearances and applications in many other fields of physics, vector backgrounds can be used in order to incorporate mass dimension two vector condensates into gauge field theories in a Lorentz invariant way [1,2,3] or, in a different context, in theories breaking Lorentz invariance explicitely [4]. The latter approach is motivated from string [5] and non-commutative field theory [6].…”

“…A Lorentz invariant ensemble is a set of vectors which is mapped onto itself under any Lorentz transformation, while, of course, almost every single element changes. In [1,2,3] it has been demonstrated that the elementary fermions and/or bosons are removed from the spectrum of asymptotically freely propagating particles. Usually the ensembles of backgrounds used in the literature [2,3] contain gauge field configurations leading to zero as well as to non-zero field tensors.…”

“…In [1,2,3] it has been demonstrated that the elementary fermions and/or bosons are removed from the spectrum of asymptotically freely propagating particles. Usually the ensembles of backgrounds used in the literature [2,3] contain gauge field configurations leading to zero as well as to non-zero field tensors. However, the work presented in [1] shows that the propagation of fermions is already stopped in pure gauge configurations of the background in Euclidean as well as in Minkowski space.…”

“…In order to incorporate the condensates' influence, the gauge field is shifted by a background vector Φ. In general it is taken to be constant [1,2,3], thereby corresponding to the long wave-length limit of a more general approach. A homogeneous background alone does not break translational invariance.…”