Study of the nonlocal gauge invariant mass operator Tr∫d4xFμν(D2)−1Fμνin the maximal Abelian gauge

Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, Ronaldo

doi:10.1088/1751-8113/41/15/155401

“…The results here have concentrated on gauges fulfilling the perturbative Landau gauge condition. Therefore, many results in Coulomb gauge [18,85,467,468,, interpolating gauges [181,363,[501][502][503][504], linear covariant gauges [13,41,142,505,506], maximal Abelian gauges [158,505,[507][508][509][510][511][512][513][514], direct Laplacian gauges [56,[515][516][517], and other gauges [13,64,137,188,231,232,[518][519][520][521] have not been covered, though results at a similar level have been obtained in these cases as well. In particular, a similar situation with the finite-ghost case and scaling appears to be realized in Coulomb gauge [475,481,485,494], though this has to be investigated further.…”

Section: Discussionmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

Maas

¹

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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“…The results here have concentrated on gauges fulfilling the perturbative Landau gauge condition. Therefore, many results in Coulomb gauge [18,85,467,468,, interpolating gauges [181,363,[501][502][503][504], linear covariant gauges [13,41,142,505,506], maximal Abelian gauges [158,505,[507][508][509][510][511][512][513][514], direct Laplacian gauges [56,[515][516][517], and other gauges [13,64,137,188,231,232,[518][519][520][521] have not been covered, though results at a similar level have been obtained in these cases as well. In particular, a similar situation with the finite-ghost case and scaling appears to be realized in Coulomb gauge [475,481,485,494], though this has to be investigated further.…”

Section: Discussionmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

Maas

2011

Preprint

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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A potential setup for perturbative confinement

Dudal

¹

2009

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A few years ago, 't Hooft suggested a way to discuss confinement in a perturbative fashion. The original idea was put forward in the Coulomb gauge at tree level. In recent years, the concept of a nonperturbative short distance linear potential also attracted phenomenological attention. Motivated by these observations, we discuss how a perturbative framework, leading to a linear piece in the potential, can be developed in a manifestly gauge and Lorentz invariant manner, which moreover enjoys the property of being renormalizable to all orders. We provide an effective action framework to discuss the dynamical realization of the proposed scenario in Yang-Mills gauge theory.Comment: 11 pages. To appear in Physics Letters

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Study of the nonlocal gauge invariant mass operator Tr∫d⁴xF_μν(D²)⁻¹F_μνin the maximal Abelian gauge

Cited by 3 publications

References 60 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

A potential setup for perturbative confinement

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