QCD Green functions in a gluon field

Hoyer, Paul; Peigné, Stéphane

doi:10.1088/1126-6708/2004/12/051

Cited by 8 publications

(22 citation statements)

References 15 publications

(19 reference statements)

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“…In [2] for gluons in background configurations with, in general, non-zero field tensor and evaluated at leading order in N c −1 no residue of freely propagating bosons is found. Already for fundamental reasons this cannot be due to the specific form of the weight.…”

Section: Euclidean Spacementioning

confidence: 91%

“…Nevertheless, the different Lorentz components of a homogeneous pure gauge background commute. The background is to transform homogeneously under gauge transformations U [2]:…”

Section: Non-abelianmentioning

confidence: 99%

“…Thus the origin of this difference with respect to [2] could be the non-zero field tensors. In the case where the Lorentz components of the background vector do not commute-i.e.…”

Section: Euclidean Spacementioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Non-Abelian vector backgrounds with restored Lorentz invariance

Dietrich¹

2006

Phys. Rev. D

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The influence of vector backgrounds with restored Lorentz invariance on non-abelian gauge field theories is studied. Lorentz invariance is ensured by taking the average over a Lorentz invariant ensemble of background vectors. Like in the abelian case [1], the propagation of fermions is suppressed over long distances. Contrary to the fermionic sector, pure gauge configurations of the background suppress the long-distance propagation of the bosons only partially, i.e. not beyond the leading contribution for a large number of colours.

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Section: Euclidean Spacementioning

confidence: 91%

“…Nevertheless, the different Lorentz components of a homogeneous pure gauge background commute. The background is to transform homogeneously under gauge transformations U [2]:…”

Section: Non-abelianmentioning

confidence: 99%

“…Thus the origin of this difference with respect to [2] could be the non-zero field tensors. In the case where the Lorentz components of the background vector do not commute-i.e.…”

Section: Euclidean Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-Abelian vector backgrounds with restored Lorentz invariance

Dietrich¹

2006

Phys. Rev. D

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“…(2.9) below). In [3,4] we showed that the modification (1.3) can be obtained by assuming a constant background field and averaging over all components of this field with a gaussian weight. It was possible to calculate exactly the dressed quark and gluon propagators in the limit of a large number of colors (N c → ∞), i.e., for all planar Feynman diagrams.…”

Section: Introductionmentioning

confidence: 99%

Perturbative gauge theory in a background

Dietrich¹,

Hoyer

Järvinen

et al. 2007

AIP Conference Proceedings

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Motivated by the gluon condensate in QCD we study the perturbative expansion of a gauge theory in the presence of gauge bosons of vanishing momentum, in the specific case of an abelian theory. The background is characterised by a dimensionful parameter Λ affecting only the on-shell prescription of the free (abelian) gluon propagator. When summed to all orders in gΛ the modification is equivalent to evaluating standard Green functions in a pure gauge field with an imaginary gauge parameter ∝ Λ. We show how to calculate the corresponding dressed Green functions, which are Poincaré and gauge covariant. We evaluate the expressions for the dressed quark and qq propagators, imposing as boundary condition that they approach the standard perturbative form in the short-distance limit (|p 2 | → ∞). The on-shell (p 2 = m 2 ) pole of the free quark propagator is removed for any Λ > 0, and replaced by a discontinuity which vanishes exponentially with p 2 . The dressing introduces an effective interaction between quarks and antiquarks which is enhanced at low relative 3-momentum. Further study should allow to identify the (bound) eigenstates of propagation and determine whether they define a unitary S-matrix. When the quark mass is zero there is a euclidean propagator solution which breaks chiral symmetry spontaneously. We study some aspects of the massless pion contribution to axial vector correlators and derive the πqq form factor.

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Lorentz-invariant ensembles of vector backgrounds

Dietrich¹,

Hofmann

2006

Physics Letters B

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We consider gauge field theories in the presence of ensembles of vector backgrounds. While Lorentz invariance is explicitely broken in the presence of any single background, here, the Lorentz invariance of the theory is restored by averaging over a Lorentz invariant ensemble of backgrounds, i.e. a set of background vectors that is mapped onto itself under Lorentz transformations. This framewkork is used to study the effects of a non-trivial but Lorentz invariant vacuum structure or mass dimension two vector condensates by identifying the background with a shift of the gauge field. Up to now, the ensembles used in the literature comprise configurations corresponding to non-zero field tensors together with such with vanishing field strength. We find that even when constraining the ensembles to pure gauge configurations, the usual high-energy degrees of freedom are removed from the spectrum of asymptotic states in the presence of said backgrounds in euclidean and in Minkowski space. We establish this result not only for the propagators to all orders in the background and otherwise at tree level but for the full propagator.

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QCD Green functions in a gluon field

Cited by 8 publications

References 15 publications

Non-Abelian vector backgrounds with restored Lorentz invariance

Non-Abelian vector backgrounds with restored Lorentz invariance

Perturbative gauge theory in a background

Lorentz-invariant ensembles of vector backgrounds

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