General theory of renormalization of gauge invariant operators

Joglekar, Satish D.; Lee, Benjamin W

doi:10.1016/0003-4916(76)90225-6

Cited by 232 publications

(188 citation statements)

References 4 publications

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“…[16]. We found (in complete agreement with Pagels [14]) that even at zero momentum transfer no useful information can be obtained, indeed.…”

Section: A Ghost-gluon Vertexsupporting

confidence: 85%

See 1 more Smart Citation

Two-dimensional QCD in the covariant gauge

Gogokhia¹,

Kluge²

2002

Phys. Rev. D

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A nonperturbative approach to 2D covariant gauge QCD is presented in the context of the Schwinger-Dyson equations for quark and ghost propagators and the corresponding Slavnov-Taylor identities. The distribution theory, complemented by the dimensional regularization method, is used in order to correctly treat the severe infrared singularities which inevitably appear in the theory. By working out the multiplicative renormalization program we remove them from the theory on a general ground and in a self-consistent way, proving thus the infrared multiplicative renormalizability of 2D QCD within our approach. This makes it possible to sum up the infinite series of the corresponding planar skeleton diagrams in order to derive a closed set of equations for the infrared renormalized quark propagator. We have shown that complications due to ghost degrees of freedom can be considerable within our approach. It is shown exactly that 2D covariant gauge QCD implies quark confinement (the quark propagator has no poles, indeed) as well as dynamical breakdown of chiral symmetry (a chiral symmetry preserving solution is forbidden). We also show explicitly how to formulate the bound-state problem and the Schwinger-Dyson equations for the gluon propagator and the triple gauge proper vertex, all free of the severe IR singularities.

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“…[16]. We found (in complete agreement with Pagels [14]) that even at zero momentum transfer no useful information can be obtained, indeed.…”

Section: A Ghost-gluon Vertexsupporting

confidence: 85%

“…Passing to the IR renormalized quantities, one obtains 16) so that the following IR convergence relation holds…”

Section: B Ir Finite St Identities For Pure Gluon Verticesmentioning

confidence: 99%

Two-dimensional QCD in the covariant gauge

Gogokhia¹,

Kluge²

2002

Phys. Rev. D

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“…As is well known doing otherwise can lead to erroneous anomalous dimensions. (See, for example, [5,6,7].) Moreover, we will show that one cannot readily drop operators which are total space-time derivatives of lower dimensional operators but which are overall dimension six.…”

Section: Introductionmentioning

confidence: 84%

“…This is achieved by respecting the standard renormalization theorems, [5,6,7]. In essence each operator is inserted in a Green's function with the same number of external legs as the operator itself.…”

Section: One Loop Renormalizationmentioning

confidence: 99%

Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics

Gracey

2002

Nuclear Physics B

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“…Such a conjecture was first proved for Yang-Mills theories in ref. [6]. There, the usual Lorentz gauge was used.…”

Section: Introductionmentioning

confidence: 99%

More on the subtraction algorithm

Anselmi

1995

Class. Quantum Grav.

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We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions δλ of the parameters λ of the classical Lagrangian and canonical transformations. The key point is to generalize a well-known conjecture on the form of the divergent terms to the case of open gauge-algebrae. We also show that it is possible to reach a complete control on the effects of the subtraction algorithm on the space M gf of the gauge-fixing parameters. We develop a differential calculus on M gf providing an intuitive geometrical description of the fact the on shell physical amplitudes cannot depend on M gf . A principal fiber bundle E → M gf with a connection ω 1 is defined, such that the canonical transformations are gauge transformations for ω 1 . A geometrical description of the effect of the subtraction algorithm on the space M ph of the physical parameters λ is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on M ph , orthogonal to M gf (under which the action transforms as a scalar), and gauge transformations on E. In this geometrical context, a suitable concept of predictivity is formulated. Finally, we give some examples of (unphysical) toy models that satisfy this requirement, though being neither power counting renormalizable, nor finite.

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General theory of renormalization of gauge invariant operators

Cited by 232 publications

References 4 publications

Two-dimensional QCD in the covariant gauge

Two-dimensional QCD in the covariant gauge

Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics

More on the subtraction algorithm

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