Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notational conventions
- Note added in proof: the discovery of the top quark (?)
- Note added in proof: the demise of the SSC
- 18 Determination of the Kobayashi–Maskawa matrix
- 19 Mixing and CP violation
- 20 Regularization, renormalization and introduction to the renormalization group
- 21 Gauge theories, QCD and the renormalization group
- 22 Applications of the QCD renormalization group
- 23 The parton model in QCD
- 24 Large pT phenomena and jets in hadronic reactions
- 25 Jets and hadrons in e+e− physics
- 26 Low pT or ‘soft’ hadronic physics
- 27 Some non-perturbative aspects of gauge theories
- 28 Beyond the standard model
- Appendix 1 Elements of field theory
- Appendix 2 Feynman rules for QED, QCD and the SM
- Appendix 3 Conserved vector currents and their charges
- Appendix 4 Operator form of Feynman amplitudes and effective Hamiltonians
- Appendix 5 S-matrix, T-matrix and Feynman amplitude
- Appendix 6 Consequences of CPT invariance for matrix elements
- Appendix 7 Formulae for the basic partonic 2 → 2 processes
- Appendix 8 Euclidean space conventions
- References
- Analytic subject index for vols. 1 and 2
20 - Regularization, renormalization and introduction to the renormalization group
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notational conventions
- Note added in proof: the discovery of the top quark (?)
- Note added in proof: the demise of the SSC
- 18 Determination of the Kobayashi–Maskawa matrix
- 19 Mixing and CP violation
- 20 Regularization, renormalization and introduction to the renormalization group
- 21 Gauge theories, QCD and the renormalization group
- 22 Applications of the QCD renormalization group
- 23 The parton model in QCD
- 24 Large pT phenomena and jets in hadronic reactions
- 25 Jets and hadrons in e+e− physics
- 26 Low pT or ‘soft’ hadronic physics
- 27 Some non-perturbative aspects of gauge theories
- 28 Beyond the standard model
- Appendix 1 Elements of field theory
- Appendix 2 Feynman rules for QED, QCD and the SM
- Appendix 3 Conserved vector currents and their charges
- Appendix 4 Operator form of Feynman amplitudes and effective Hamiltonians
- Appendix 5 S-matrix, T-matrix and Feynman amplitude
- Appendix 6 Consequences of CPT invariance for matrix elements
- Appendix 7 Formulae for the basic partonic 2 → 2 processes
- Appendix 8 Euclidean space conventions
- References
- Analytic subject index for vols. 1 and 2
Summary
Our eventual aim is a simple and intelligible discussion of QCD and its applications to deep inelastic scattering, the Drell–Yan process and the cross-section for e+e− → hadrons etc. To achieve this, in this chapter we present a heuristic treatment of the ideas of regularization, renormalization and the powerful renormalization group technique. Then we introduce the concept of scaling and asymptotic freedom, initially for the case of scalar particles. The renormalization group results derived for scalar particles will be extended to the realistic case in Chapter 21, and applications, follow in Chapter 22. All technical elements are relegated to the Appendix to this chapter (Section 20.10) where we explain the technique of dimensional regularization.
Introduction
Most discussions of renormalization theory, in textbooks on field theory, are impenetrable and bogged down in technical complexities. Previously this did not matter very much. The important thing was to know that the theory was renormalizable, and the calculation of a few important effects could be left to a handful of experts. But the realization of the importance of the renormalization group in perturbative QCD and its constant use in all calculations of hard hadronic processes has meant that it is essential to understand at least the main ideas about schemes of regularization and renormalization.
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- Publisher: Cambridge University PressPrint publication year: 1996