Lorentz-invariant ensembles of vector backgrounds

Dietrich, Dennis D.; Hofmann, Stefan

doi:10.1016/j.physletb.2005.10.071

“…The correlator is obtained by contracting the axial vector vertex (5.12) with γ 5 . The loop integral is well-defined after a Wick rotation 4 Tr e − k2 /(2µ 2 ) / pγ 5 γ ν γ 5 − e −k 2 /(2µ 2 ) γ 5 / pγ ν γ 5 eucl.…”

Section: Spontaneous Chiral Symmetry Breakingmentioning

confidence: 99%

“…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

²

,

Järvinen

³

et al. 2007

J. High Energy Phys.

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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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“…(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

²

,

Järvinen

³

et al. 2007

AIP Conference Proceedings

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0

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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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Non-Abelian vector backgrounds with restored Lorentz invariance

Dietrich¹

2006

Phys. Rev. D

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0

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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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Lorentz-invariant ensembles of vector backgrounds

Cited by 5 publications

References 25 publications

Perturbative gauge theory in a background

Perturbative gauge theory in a background

Perturbative gauge theory in a background

Non-Abelian vector backgrounds with restored Lorentz invariance

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