Analytical study of Yang–Mills theory in the infrared from first principles

Siringo, Fabio

doi:10.1016/j.nuclphysb.2016.04.028

Cited by 80 publications

(178 citation statements)

References 38 publications

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“…In this section we include a set of chiral quarks in the massive expansion that has been recently developed for pure Yang Mills theory [32,46,47]. While the inclusion of bare masses for the quarks would be straightforward, we prefer to deal with the chiral limit in this paper for several reasons.…”

Section: The Massive Expansion In the Chiral Limitmentioning

confidence: 99%

“…[47] a shift of the pole in the propagators can be introduced by an unconventional splitting of the total action. We may add and subtract the arbitrary terms δS g , δS q in the total action…”

Section: The Massive Expansion In the Chiral Limitmentioning

confidence: 99%

“…Since δS q and δS g are added and subtracted again, the total action cannot depend on the masses, but any expansion in powers of the new shifted interaction S I → S I − δS q − δS g is going to depend on them at any finite order because of the truncation. Thus, while we are not changing the content of the theory, the emerging perturbative approximation is going to depend on the masses and can be optimized by a choice of m and M that minimizes the effects of higher orders, yielding a variational tool disguised to look like a perturbative method [47]. The idea is not new and goes back to the works on the Gaussian effective potential [49,[59][60][61][62][63][64][65][66] where an unknown mass parameter was inserted in the zeroth order propagator and subtracted from the interaction, yielding a pure variational approximation with the mass that acts as a variational parameter.…”

Section: The Massive Expansion In the Chiral Limitmentioning

confidence: 99%

“…Quite recently, an analytical approach has been proposed that is based on a different expansion point for the exact Lagrangian of pure Yang-Mills theory in the Landau gauge [46,47]. The new expansion is around a massive free-particle propagator, yielding a massive loop expansion with massive particles in the internal lines of the Feynman graphs.…”

Section: Introductionmentioning

confidence: 99%

“…[47] is extended to chiral QCD in the Landau gauge; in Section III, the case of pure Yang-Mills theory is examined, the propagators are continued to Minkowski space and their spectral density is studied in detail; in Section IV, the full chiral QCD is discussed, a dynamical mass is obtained for the quarks and compared with the lattice data in the Euclidean space, the spectral functions are derived for ghosts, gluons and quarks; in Section V the main results of the paper are discussed. The explicit analytical expressions of the propagators are derived in the Appendix.…”

Section: Introductionmentioning

confidence: 99%

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Analytic structure of QCD propagators in Minkowski space

Siringo

2016

Phys. Rev. D

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105

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Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, deep in the infrared. By analytic continuation, the spectral functions are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles.The dynamical breaking of chiral symmetry is described on the same footing of gluon mass generation, providing a unified picture. While dealing with the exact Lagrangian, the expansion is based on massive free-particle propagators, is safe in the infrared and is equivalent to the standard perturbation theory in the UV. By dimensional regularization, all diverging mass terms cancel exactly without including mass counterterms that would spoil the gauge and chiral symmetry of the Lagrangian. Universal scaling properties are predicted for the inverse dressing functions and shown to be satisfied by the lattice data. Complex conjugated poles are found for the gluon propagator, in agreement with the i-particle scenario.

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Section: The Massive Expansion In the Chiral Limitmentioning

confidence: 99%

Section: The Massive Expansion In the Chiral Limitmentioning

confidence: 99%

Section: The Massive Expansion In the Chiral Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytic structure of QCD propagators in Minkowski space

Siringo

2016

Phys. Rev. D

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105

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From Condensed Matter to QCD: A Journey Through Gauge Theories on Board of a Variational Tool

Siringo

2017

Correlations in Condensed Matter Under Extreme Conditions

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Starting with a review of the thermal fluctuations in superconductors, the Gaussian Effective Potential is shown to be a powerful variational tool for the study of the breaking of symmetry in gauge theories. A novel re-derivation of the massive expansion for QCD is presented, showing its variational nature and its origin from the Gaussian potential that also provides a variational proof for chiral symmetry breaking and dynamical generation of a gluon mass.

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On a renormalizable class of gauge fixings for the gauge invariant operatorAmin2

et al. 2018

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The dimension two gauge invariant non-local operator A 2 min , obtained through the minimization of d 4 xA 2 along the gauge orbit, allows to introduce a non-local gauge invariant configuration A h µ which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both A 2 min and A h µ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of A 2 min gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as 't Hooft's R ζ -gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field. *

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Analytical study of Yang–Mills theory in the infrared from first principles

Cited by 80 publications

References 38 publications

Analytic structure of QCD propagators in Minkowski space

Analytic structure of QCD propagators in Minkowski space

From Condensed Matter to QCD: A Journey Through Gauge Theories on Board of a Variational Tool

On a renormalizable class of gauge fixings for the gauge invariant operatorAmin2

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