Consistent perturbative light front formulation of Yang-Mills theories

Morara, M.; Soldati, Roberto; McCartor, Gary

doi:10.1063/1.1301673

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…of (regularization-dependent) ghost degrees of freedom in the original theory. The dimensional regularization procedure along with the ML prescription may also give rise to the additional (hidden regularization-dependent) ghost contributions to the divergent integrals [38]. The noncovariant ln(−2q + q − ) contribution in Eq.…”

Section: Gluon Propagatormentioning

confidence: 99%

Light-front-quantized QCD in the light-cone gauge: The doubly transverse gauge propagator

Srivastava

Brodsky

2001

Phys. Rev. D

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The light-front ͑LF͒ quantization of QCD in the light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high-momentum transfer inclusive and exclusive reactions. We present a systematic study of LF-quantized gauge theory following the Dirac method, and construct a Dyson-Wick S-matrix expansion based on LF time-ordered products. The free theory gauge field is shown to satisfy the Lorentz condition as an operator equation as well as the light-cone gauge condition. Its propagator is found to be transverse with respect to both its 4 momentum and the gauge direction. The interaction Hamiltonian of QCD can be expressed in a form resembling that of covariant theory, except for additional instantaneous interactions which can be treated systematically. The renormalization constants in YM theory are shown to satisfy the identity Z 1 ϭZ 3 at one-loop order. The QCD ␤ function, computed in the noncovariant light-cone gauge, agrees with that known in the conventional framework. Some comments are also made about the relationship of our LF framework, with a doubly transverse gauge propagator, to the analytic effective charge and renormalization scheme defined by the pinch technique, the unitarity relations, and the spectral representation. LF quantization thus provides a consistent formulation of gauge theory, despite the fact that the hyperplanes x Ϯ ϭ0 used to impose boundary conditions constitute characteristic surfaces of a hyperbolic partial differential equation.

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Section: Gluon Propagatormentioning

confidence: 99%

Light-front-quantized QCD in the light-cone gauge: The doubly transverse gauge propagator

Srivastava

Brodsky

2001

Phys. Rev. D

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“…However, some problems were associated with such gauge choice: Feynman amplitudes at the one-loop level exhibited double-pole singularities [18]. This pathological behavior has been ascribed to the Principal Value (PV) prescription employed to treat the unphysical poles (k · n) −1 of the gauge boson propagator [19], though application of dimensional regularization to one-loop integrals does also yield double poles [18,20]: These double poles appeared to be prescription independent.…”

mentioning

confidence: 96%

Functional Analysis for Gauge Fields on the Front-Form and the Light-Cone Gauge

2011

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Constrained systems in quantum field theories call for a careful study of diverse classes of constraints and consistency checks over their temporal evolution. Here we study the functional structure of the free electromagnetic and pure Yang-Mills fields on the front-form coordinates with the null-plane gauge condition. It is seen that in this framework, we can deal with strictu sensu physical fields.

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“…It was also shown a long time ago [55] that the Pauli-Villars method of regularization corresponds to the introduction of (regularization-dependent) ghost degrees of freedom in the original theory. The dimensional regularization procedure along with the ML prescription may also give rise to the additional (hidden regularization-dependent) ghost contributions to the divergent integrals [38]. The noncovariant ln(−2q + q − ) contribution in Eq.…”

Section: Appendix Cmentioning

confidence: 99%

Light-Front-Quantized QCD in Light-Cone Gauge

Brodsky¹

2000

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The light-front (LF) quantization of QCD in light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. We present a systematic study of LF-quantized gauge theory following the Dirac method and construct the Dyson-Wick S-matrix expansion based on LF-time-ordered products. The free theory gauge field is shown to satisfy the Lorentz condition as an operator equation as well as the light-cone gauge condition. Its propagator is found to be transverse with respect to both its four-momentum and the gauge direction. The interaction Hamiltonian of QCD can be expressed in a form resembling that of covariant theory, except for additional instantaneous interactions which can be treated systematically. The renormalization constants in YM theory are shown to satisfy the identity Z 1 = Z 3 at one loop order. The QCD β function computed in the noncovariant light-cone gauge agrees with that known in the conventional framework. Some comments on the relationship of our LF framework, with the doubly transverse gauge propagator, to the analytic effective charge and renormalization scheme defined by the pinch technique, the unitarity relations and the spectral representation are also made. LF quantization thus provides a consistent formulation of gauge theory, despite the fact that the hyperplanes x ± = 0 used to impose boundary conditions constitute characteristic surfaces of a hyperbolic partial differential equation.

show abstract

Consistent perturbative light front formulation of Yang-Mills theories

Cited by 3 publications

References 16 publications

Light-front-quantized QCD in the light-cone gauge: The doubly transverse gauge propagator

Light-front-quantized QCD in the light-cone gauge: The doubly transverse gauge propagator

Functional Analysis for Gauge Fields on the Front-Form and the Light-Cone Gauge

Light-Front-Quantized QCD in Light-Cone Gauge

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