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Canonical Formulation of the Light-Front Gluodynamics and Quantization of the Non-Abelian Plane Waves
High Energy Physics - Theory · Submitted 20 Oct 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves.
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The abstract, sentence by sentence
Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. | contribution 0.68 | 0.88 | 0.11 | asserted 1.00 |
| s1 | The Gauss law is written in terms of the canonical variables. | contribution 0.61 | 0.87 | 0.04 | asserted 1.00 |
| s2 | The system is qualified as a generalized dynamical system with first class constraints. | result 0.71 | 0.82 | 0.08 | asserted 1.00 |
| s3 | Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). | result 0.85 | 0.77 | 0.08 | asserted 1.00 |
| s4 | At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. | result 1.00 | 0.92 | 0.12 | asserted 1.00 |
| s5 | We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. | result 0.90 | 0.94 | 0.49 | asserted 1.00 |
| s6 | Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. | interpretation 0.61 | 0.95 | 0.20 | hedged possibility 0.86 |
| s7 | We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges. | result 0.91 | 0.89 | 0.07 | asserted 0.88 |
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Original abstract
Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.
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