Book contents
- Frontmatter
- Contents
- About Stephan Narison
- Outline of the book
- Preface
- Acknowledgements
- Part I General introduction
- Part II QCD gauge theory
- 5 Lagrangian and gauge invariance
- 6 Quantization using path integral
- 7 QCD and its global invariance
- Part III MS-bar scheme for QCD and QED
- Part IV Deep inelastic scatterings at hadron colliders
- Part V Hard processes in e+e– collisions
- Part VI Summary of QCD tests and αs measurements
- Part VII Power corrections in QCD
- Part VIII QCD two-point functions
- Part IX QCD non-perturbative methods
- Part X QCD spectral sum rules
- Part XI Appendices
- Bibliography
- Index
5 - Lagrangian and gauge invariance
from Part II - QCD gauge theory
- Frontmatter
- Contents
- About Stephan Narison
- Outline of the book
- Preface
- Acknowledgements
- Part I General introduction
- Part II QCD gauge theory
- 5 Lagrangian and gauge invariance
- 6 Quantization using path integral
- 7 QCD and its global invariance
- Part III MS-bar scheme for QCD and QED
- Part IV Deep inelastic scatterings at hadron colliders
- Part V Hard processes in e+e– collisions
- Part VI Summary of QCD tests and αs measurements
- Part VII Power corrections in QCD
- Part VIII QCD two-point functions
- Part IX QCD non-perturbative methods
- Part X QCD spectral sum rules
- Part XI Appendices
- Bibliography
- Index
Summary
Introduction
After Einstein's identification of the invariance group of space and time in 1905, symmetry principles received an enthusiastic welcome in physics, with the hope that these principles could express the simplicity of nature in its deepest level. Since 1927 [99,100], it has been recognized that Quantum ElectroDynamics (QED) has a local symmetry under the transformations in which the electron field has a phase change that can vary point to point in space–time, and the electromagnetic vector potential undergoes a corresponding transformation. This kind of transformation is called a U(1) gauge symmetry due to the fact that a simple phase change can be thought as a multiplication by a 1 × 1 unitary matrix. Largely motivated by the challenge of giving a field-theoretical framework to the concept of isospin invariance, Yang and Mills [101] in 1954 extended the idea of QED to the SU(2) group of symmetry. However, it appears here that the symmetry would have to be approximate because gauge invariance requires massless vector bosons like the photon, and it seems obvious that strong interactions of pions were not mediated by massless but by the massive ρ mesons. In 1961, there was the idea of dynamic breaking, i.e., the Hamiltonian and commutation relations of a quantum theory could possess an exact symmetry and the symmetry of the Hamiltonian might not turn to be a symmetry of the vacuum.
- Type
- Chapter
- Information
- QCD as a Theory of HadronsFrom Partons to Confinement, pp. 57 - 62Publisher: Cambridge University PressPrint publication year: 2004