Lavelle and McMullan Reply

Lavelle, Martin; McMullan, David

doi:10.1103/physrevlett.73.1048

Cited by 104 publications

(295 citation statements)

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“…The first non-trivial test of QCD dressings was a study of the interquark potential presented in [10]. Here it was shown that the minimal gauge-invariant extension to QCD of the dressing appropriate to a static charge in QED exactly describes the gluonic configuration which is responsible for asymptotic freedom and anti-screening.…”

Section: Discussionmentioning

confidence: 99%

“…Since any description of a physical charged particle is necessarily both non-local and non-covariant, it is important to study the renormalisability of these variables 10 . Similarly we have studied the infra-red problem which, as we argued in I, results from the non-trivial asymptotic dynamics which is not properly included in the Green's functions of unphysical asymptotic fields.…”

Section: Discussionmentioning

confidence: 99%

“…As well as identifying the above mentioned limit on the construction of observable quarks and constructing solutions for dressed electrons, quarks and gluons (the last two in perturbation theory) which have a specific physical identification, the notable successes of this programme include the demonstration, in QED, that the dressed Green's functions for charge propagation possess a good pole structure [8,9], that S-matrix elements for interactions with dressed asymptotic fields are free of on-shell IR divergences [5] and that the paradigm anti-screening behaviour of QCD can be understood in terms of the interaction between two separately gauge-invariant coloured quarks [10].…”

Section: Introductionmentioning

confidence: 99%

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Charges from Dressed Matter: Physics and Renormalisation

2000

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Gauge theories are characterised by long range interactions. Neglecting these interactions at large times, and identifying the Lagrangian matter fields with the asymptotic physical fields, leads to the infra-red problem. In this paper we study the perturbative applications of a construction of physical charges in QED, where the matter fields are combined with the associated electromagnetic clouds. This has been formally shown, in a companion paper, to include these asymptotic interactions. It is explicitly demonstrated that the on-shell Green's functions and S-matrix elements describing these charged fields have, to all orders in the coupling, the pole structure associated with particle propagation and scattering. We show in detail that the renormalisation procedure may be carried out straightforwardly. It is shown that standard infra-red finite predictions of QED are not altered and it is speculated that the good infra-red properties of our construction may open the way to the calculation of previously uncalculable properties. Finally extensions of this approach to QCD are briefly discussed.1 email: bagan@quark.phy.bnl.gov; permanent address: IFAE, Univ.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Charges from Dressed Matter: Physics and Renormalisation

2000

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“…The key to this direction would be to notice the Gribov ambiguity [20]: in a smaller region, the Coulomb gauge is well-defined, that is, no gauge degrees of freedom being left owing to the asymptotic freedom. The larger a region, however, the more nontrivial degree comes into a part [21]. Since gauge invariance is essential to comprehend the quark confinement, the path integral must be useful.…”

Section: Discussionmentioning

confidence: 99%

Gauge independence in terms of the functional integral

Kashiwa

Tanimura

1997

Phys. Rev. D

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Among various approaches in proving gauge independence, models containing an explicit gauge dependence are convenient. The well-known example is the gauge parameter in the covariant gauge fixing which is of course most suitable for the perturbation theory but a negative metric prevents us from imaging a dynamical picture. Noncovariant gauge such as the Coulomb gauge is on the contrary used for many physical situations. Therefore it is desirable to include both cases. More than ten years ago, Steinmann introduced a function (distribution) which can play this role in his attempt on discussing quantum electrodynamics (QED) in terms of the gauge invariant fields solely. The method is, however, broken down in the covariant case: the invariant operators are ill-defined because of 1/p 2 singularity in the Minkowski space. In this paper, we apply his function to the path integral: utilizing the arbitrariness of the function we first restrict it to be able to have a well-defined operator, and then a Hamiltonian with which we can build up the (Euclidean) path integral formula. Although the formula is far from covariant, a full covariant expression is recovered by reviving the components which have been discarded under the construction of the Hamiltonian. There is no pathological defects contrary to the operator formalism. With the aid of the path integral formula, the gauge independence of the free energy as well as the S-matrix is proved. Moreover the reason is clarified why it is so simple and straightforward to argue gauge transformations in the path integral. Discussions on the quark confinement is also presented.

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“…Finally in QCD confinement shows that the interaction does not switch off and the strong interaction between quarks and gluons is indeed supposed to grow with the separation. The application of the methods of asymptotic dynamics and the construction of physical fields at short distances [21,22] could have implications for jets production. It has though been demonstrated that there is a topological obstruction to the construction of an isolated quark or gluon [22], how this relates to non-perturbative effects in the asymptotic dynamics of QCD is a topic for future work.…”

Section: Discussionmentioning

confidence: 99%

Asymptotic dynamics in quantum field theory

Horan

Lavelle

McMullan

2000

Journal of Mathematical Physics

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A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynamics in field theories which incorporates the important features of weak convergence and physical boundary conditions. Applications to theories with three and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory.

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Lavelle and McMullan Reply

Cited by 104 publications

References 4 publications

Charges from Dressed Matter: Physics and Renormalisation

Charges from Dressed Matter: Physics and Renormalisation

Gauge independence in terms of the functional integral

Asymptotic dynamics in quantum field theory

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