Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 An introduction to unitary symmetry
- 2 Soft pions
- 3 Dilatations
- 4 Renormalization and symmetry: a review for non-specialists
- 5 Secret symmetry: an introduction to spontaneous symmetry breakdown and gauge fields
- 6 Classical lumps and their quantum descendants
- 7 The uses of instantons
- 8 1/N
3 - Dilatations
Published online by Cambridge University Press: 10 November 2010
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 An introduction to unitary symmetry
- 2 Soft pions
- 3 Dilatations
- 4 Renormalization and symmetry: a review for non-specialists
- 5 Secret symmetry: an introduction to spontaneous symmetry breakdown and gauge fields
- 6 Classical lumps and their quantum descendants
- 7 The uses of instantons
- 8 1/N
Summary
Introduction
It is an old idea in particle physics that, in some sense, at sufficiently high energies the masses of the elementary particles should become unimportant. In recent years this somewhat vague hope has acquired a more definite form in the theory of scale transformations, or dilatations. These are transformations that would be exact invariances of the world if all elementary particle masses (more generally, all dimensionful couplings) vanished. The hope is that, by studying these approximate symmetries in Lagrangian field theories, we can gain knowledge about how scale transformations behave in the real world, and learn something about those kinematic realms where the effects of masses are indeed unimportant, or at least simply calculable. This is a hope that has been fulfilled for broken chiral symmetries, by the study of models such as the sigma-model.
The purpose of these lectures is to report on the progress of such investigations. As we shall see, there is still much that is obscure. In particular, the connection between the sorts of things I will be talking about and the famous experimental scaling of deep inelastic electroproduction remains to be unravelled. Nevertheless, what has been done so far has already yielded some remarkable theoretical surprises.
Section 2 is a description of the formal Lagrangian theory of scale transformations. Some of the Ward identities that express broken scale invariance are derived, models of Nambu–Goldstone scale-symmetry breaking are discussed, and the connection between scale invariance and conformal invariance is explained.
- Type
- Chapter
- Information
- Aspects of SymmetrySelected Erice Lectures, pp. 67 - 98Publisher: Cambridge University PressPrint publication year: 1985
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