Elements of Quantum Field Theory

Zavialov, O. I.

doi:10.1007/978-94-009-2585-4_1

Cited by 30 publications

(42 citation statements)

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“…So it is possible to apply the light-cone expansion of the current product. Instead of the standard expansion in terms of local operators we use the more effective expansion based on light-ray operators [12,22]. This expansion relies on a perturbative expansion of the product of the electromagnetic currents, too.…”

Section: Appendix A: Virtual Compton Scattering Amplitude In Leading mentioning

confidence: 99%

“…The anomalous dimension can be determined from the 1PI vertex function of the operator to be studied [22,24]. For instance, by using dimensional regularization it can be shown that in the minimal subtraction scheme the following simple rule is valid [29] γ(κ, κ…”

Section: Appendix B: Properties Of Anomalous Dimensions Of Light-ray mentioning

confidence: 99%

“…With these remarks the α-representation for a 1PI diagram with L internal lines and V vertices and two external legs can be written as [22] …”

Section: Appendix B: Properties Of Anomalous Dimensions Of Light-ray mentioning

confidence: 99%

“…[22]; furthermore, in contrast to Ref. [22] we have absorbed the overall factor 1/D of the exponent into the definition of A ij , B li and K kl . Anyway, the coefficients A ij , B li and K kl may be simply deduced from the general rules given there.…”

Section: Appendix B: Properties Of Anomalous Dimensions Of Light-ray mentioning

confidence: 99%

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Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD

et al. 1994

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The widely used nonperturbative wave functions and distribution functions of QCD are determined as matrix elements of light-ray operators. These operators appear as large momentum limit of nonlocal hadron operators or as summed up local operators in light-cone expansions. Nonforward one-particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. These distribution functions depend besides other variables on two scaling variables. They are applied for the description of exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes are derived on the basis of the renormalization group equation of the considered operators. This includes that also the evolution kernels follow from the anomalous dimensions of these operators. Relations between different evolution kernels (especially the Altarelli-Parisi and the Brodsky-Lepage) kernels are derived and explicitly checked for the existing two-loop calculations of QCD. Technical basis of these results are support and analytically properties of the anomalous dimensions of light-ray operators obtained with the help of the α-representation of Green's functions.

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Section: Appendix A: Virtual Compton Scattering Amplitude In Leading mentioning

confidence: 99%

Section: Appendix B: Properties Of Anomalous Dimensions Of Light-ray mentioning

confidence: 99%

“…With these remarks the α-representation for a 1PI diagram with L internal lines and V vertices and two external legs can be written as [22] …”

Section: Appendix B: Properties Of Anomalous Dimensions Of Light-ray mentioning

confidence: 99%

Section: Appendix B: Properties Of Anomalous Dimensions Of Light-ray mentioning

confidence: 99%

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Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD

et al. 1994

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“…For the further analysis, it is very convenient to transform the integral in (13) into the -representation (see [71,72]), which is one of the basic methods for the study of hard processes in perturbative QCD [73], as well as in nonperturbative quark models [33]. The technical advantage of this method is the explicit maintenance of the Lorentz covariance.…”

Section: B Calculation Of the Triangle Diagrammentioning

confidence: 99%

Generalized quark transversity distribution of the pion in chiral quark models

2011

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The transversity generalized parton distributions (tGPDs) of the pion, involving matrix elements of the tensor bilocal quark current, are analyzed in chiral quark models. We apply the nonlocal chiral models involving a momentum-dependent quark mass, as well as the local Nambu-Jona-Lasinio with the Pauli-Villars regularization to calculate the pion tGPDs, as well as related quantities following from restrained kinematics, evaluation of moments, or taking the Fourier-Bessel transforms to the impact-parameter space. The obtained distributions satisfy the formal requirements, such as proper support and polynomiality, following from Lorentz covariance. We carry out the leading-order QCD evolution from the low quark-model scale to higher lattice scales, applying the method of Kivel and Mankiewicz. We evaluate several lowest-order generalized transversity form factors, accessible from the recent lattice QCD calculations. These form factors, after evolution, agree properly with the lattice data, in support of the fact that the spontaneously broken chiral symmetry is the key element also in the evaluation of the transversity observables.

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Perturbative renormalization of composite operators via flow equations II: Short distance expansion

Keller

Kopper

1993

Commun.Math. Phys.

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We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive Φ^ The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. 2) ^ 0); 2.4. The renormalization conditions (D (1>2) ^ 0); 2.5. Perturbative renormalizability 3. Normal Products and Some (Generalized) Zimmermann Identities 3.1. Generating functionals and their flow equations; 3.2. Definition of bilocal normal products; 3.3. Lowenstein rules, Zimmermann identities 4. Short Distance Expansion 4.1. Principal part of the short distance expansion; 4.2. Example: The short distance expansion for φ(x + y)φ(x -y); 4.3. Asymptotic form of the short distance expansion; 4.4. Concluding Remarks Appendix: The proof of Theorem 2

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Elements of Quantum Field Theory

Cited by 30 publications

References 0 publications

Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD

Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD

Generalized quark transversity distribution of the pion in chiral quark models

Perturbative renormalization of composite operators via flow equations II: Short distance expansion

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