Possible Situation for Gauge Independence of Wave-Function Renormalization Constants in Gauge-Field Theories

Fukuda, Takashi; Kubo, Reijiro; Yokoyama, Keiichi

doi:10.1143/ptp.63.1384

Cited by 10 publications

(10 citation statements)

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“…This result for Z 2 was previously mentioned in [7]; in other regularization schemes the gauge dependence of Z 2 was studied in [4][5][6]. While we do not add anything new to this question in essence, we think that the derivation presented below is relatively simple and transparent and so we decided to include it into our discussion for completeness.…”

Section: Summary Of Qed Renormalization Constantsmentioning

confidence: 69%

“…[7]. Moreover, the HQET wave function renormalization constant 6 can be shown to exponentiate , i.e. it can be written as…”

Section: Hqet Wave Function Renormalizationmentioning

confidence: 99%

“…In this situation, in QED, Z 2 becomes gauge invariant to all orders in the coupling constant. This feature follows from dimensionally regulated Johnson-Zumino identity [4][5][6]:…”

Section: Introductionmentioning

confidence: 99%

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The three-loop on-shell renormalization of QCD and QED

2000

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We describe a calculation of the on-shell renormalization factors in QCD and QED at the three loop level. Explicit results for the fermion mass renormalization factor Zm and the on-shell fermion wave function renormalization constant Z2 are given. We find that at O(α 3 s ) the wave function renormalization constant Z2 in QCD becomes gauge dependent also in the on-shell scheme, thereby disproving the "gauge-independence" conjecture based on an earlier two-loop result. As a byproduct, we derive an O(α 3 s ) contribution to the anomalous dimension of the heavy quark field in HQET.

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Section: Summary Of Qed Renormalization Constantsmentioning

confidence: 69%

“…[7]. Moreover, the HQET wave function renormalization constant 6 can be shown to exponentiate , i.e. it can be written as…”

Section: Hqet Wave Function Renormalizationmentioning

confidence: 99%

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The three-loop on-shell renormalization of QCD and QED

2000

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“…By the help of this charge we can define the physical subspace CV phys as a space of states satisfying QBlphys)=0 . (3)(4)(5)(6)(7)(8)(9)(10)(11) This subsidiary condition removes the gaugeon modes as well as the unphysical photons from the physical subspace; Y and Y* together with K and K* constitute a BRST quartet.…”

Section: Ii=a+rmentioning

confidence: 99%

“…It should be noted that the q-number gauge transformation (3-12) commutes with the BRST transformation (3)(4)(5)(6)(7)(8). As a result, our BRST charge (3-10) is invariant under the q-number transformation: (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) The physical subspace CV phys is, therefore, invariant under the q-number gauge trans-formation:…”

Section: Ii=a+rmentioning

confidence: 99%

Gaugeon Formalism with BRST Symmetry

Koseki

Sato

Endo

1993

Progress of Theoretical Physics

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We provide a ERST symmetric version of Yokoyama's Type I gauge on formalism for quantum electrodynamics; the similar theory by Izawa can be considered as a ERST symmetrized Type II theory. With the help of the ERST symmetry, Yokoyama's physical subsidiary conditions are replaced by the Kugo-Ojima type condition. As a result, the formalism becomes applicable even in the background gravitational field. We show how the Hilbert spaces of standard formalism in various gauges are embedded in the single Hilbert space of the present formalism. We also give a path integral derivation of the Lagrangian. § 1. IntroductionIn the standard formalism of canonically quantized gauge theories 1 ),2) we cannot consider the gauge transformation freely. There exists no gauge freedom in the quantum theory, since the theory is defined only after the gauge fixing. Namely, a Hilbert space defined in a particular gauge is quite different from those in other gauges. Thus, if we want to realize the quantum gauge freedom, we need a wider Hilbert space.Yokoyama's gaugeon formalism 3 )-9) provides a wider framework in which we can consider the quantum gauge transformation among a family of Lorentz covariant linear gauges. In this formalism a set of extra fields, so-called gaugeon field, is introduced as the quantum gauge freedom. This theory was first proposed for the quantum electrodynamics 3 )-5) to resolve the problem of gauge parameter renormaliza· tion. )It was also applied later to the Yang-Mills theory.6),g) Thanks to the quantum gauge freedom of this formalism, the gauge parameter independence of the physical S-matrix becomes manifest. )It has also been shown, with the help of certain conjecture, that the wave-function renormalization constant is gauge independent in this formalism. S )The extra gaugeon modes should be removed from the physical Hilbert space since the quantum gauge freedom is unphysical mode. In fact the gaugeon exhibits dipole character and yields negative normed states. To remove these modes Yokoyama imposed the Gupta-Bleuler type subsidiary condition.3 )However, this type of condition does not work well if interaction is present for the gaugeon field. Especially, we cannot use Yokoyama's subsidiary condition in the background gravitational field.In the present paper we improve the subsidiary conditions of Yokoyama's formal-*) Preliminary result was reported at Niigata

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High-precision four-loop mass and wave function renormalization in QED

Laporta

2020

Physics Letters B

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The 4-loop QED mass and wave function renormalization constants Z 2 and Z m have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the QCD renormalization constants Z OS 2 and Z OS m which can obtained from QED-like diagrams. The results agree with lower precision results available in the literature. Analytical fits were also obtained for all these quantities.

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Possible Situation for Gauge Independence of Wave-Function Renormalization Constants in Gauge-Field Theories

Cited by 10 publications

References 1 publication

The three-loop on-shell renormalization of QCD and QED

The three-loop on-shell renormalization of QCD and QED

Gaugeon Formalism with BRST Symmetry

High-precision four-loop mass and wave function renormalization in QED

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