Operator ordering and Feynman rules in gauge theories

Christ, Norman H.; Lee, T. D.

doi:10.1103/physrevd.22.939

Cited by 337 publications

(488 citation statements)

References 14 publications

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“…Corresponding results for the space-time correlation functions from a Lagrangian functional integral approach are not known to this level, so one cannot proceed in analogy with Section 4. The calculations with the Lagrangian functional integral method are complicated, at the two-loop level, by the appearance of Christ-Lee-Schwinger terms [22] (see also Refs. [49,50]) which are required in order to produce results corresponding to the Hamiltonian (5) with its specific operator ordering (in particular, the insertion of powers of the Faddeev-Popov determinant).…”

Section: Discussionmentioning

confidence: 99%

“…1 represent the contraction of two elementary three-gluon vertices, the latter being given mathematically by Eq. (22). The contraction refers to spatial and color indices and the momenta, with opposite signs.…”

Section: Perturbative Vacuum Functionalmentioning

confidence: 99%

“…Indeed, in the first-order Lagrangian formalism, integrating out the A 0 -field rather than setting A 0 to zero yields an expression in the exponent of the measure for the functional integral that resembles the Christ-Lee Hamiltonian [18]. The derivation of the Hamilton operator (5) by Christ and Lee [22], on the other hand, relies on the existence of a gauge transformation that makes any gauge field A µ satisfy both the Coulomb and Weyl gauge conditions. We discuss the possibility of simultaneously implementing the Weyl and Coulomb gauges in the Hamiltonian and the Lagrangian approaches in the Appendix.…”

Section: Lagrangian Approach and Renormalizationmentioning

confidence: 99%

“…[53] for the abelian case). Subsequently, the non-abelian gauge-fixed theory can be canonically quantized with projection on the physical Hilbert space [22], or with Dirac brackets [36] enforcing all constraints strongly. Both quantization prescriptions produce the Hamiltonian operator given by Eq.…”

Section: A Gauge Transformations In Lagrangian and Hamiltonian Formalmentioning

confidence: 99%

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Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

Campagnari¹,

Weber²,

Reinhardt³

et al. 2011

Nuclear Physics B

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We apply a functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to oneloop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schrödinger equation for the vacuum wave functional to order g 2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function, and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders. *

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Section: Discussionmentioning

confidence: 99%

Section: Perturbative Vacuum Functionalmentioning

confidence: 99%

Section: Lagrangian Approach and Renormalizationmentioning

confidence: 99%

Section: A Gauge Transformations In Lagrangian and Hamiltonian Formalmentioning

confidence: 99%

See 2 more Smart Citations

Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

Campagnari¹,

Weber²,

Reinhardt³

et al. 2011

Nuclear Physics B

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“…In the constrained Hamiltonian formulation (see e.g. [2]) the time dependence of the gauge transformations (2) is exploited to put the Weyl gauge A a0 = 0 , a=1,2,3, and the physical states Ψ have to satisfy both the Schrödinger equation and the three Gauss law constraints…”

Section: Introductionmentioning

confidence: 99%

SU(2) Yang–Mills quantum mechanics of spatially constant fields

Pavel

2007

Physics Letters B

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As a first step towards a strong coupling expansion of Yang-Mills theory, the SU (2) Yang-Mills quantum mechanics of spatially constant gauge fields is investigated in the symmetric gauge, with the six physical fields represented in terms of a positive definite symmetric 3 × 3 matrix S. Representing the eigenvalues of S in terms of elementary symmetric polynomials, the eigenstates of the corresponding harmonic oscillator problem can be calculated analytically and used as orthonormal basis of trial states for a variational calculation of the Yang-Mills quantum mechanics. In this way high precision results are obtained in a very effective way for the lowest eigenstates in the spin-0 sector as well as for higher spin. Furthermore I find, that practically all excitation energy of the eigenstates, independently of whether it is a vibrational or a rotational excitation, leads to an increase of the expectation value of the largest eigenvalue φ 3 , whereas the expectation values of the other two eigenvalues, φ 1 and φ 2 , and also the component B 3 = g φ 1 φ 2 of the magnetic field, remain at their vacuum values.

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Theory of Singular Lagrangians

Cariñena

1990

Fortschr. Phys.

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Operator ordering and Feynman rules in gauge theories

Cited by 337 publications

References 14 publications

Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

SU(2) Yang–Mills quantum mechanics of spatially constant fields

Theory of Singular Lagrangians

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