8 - Renormalization group theory: its basis and formulation in statistical physics

Summary

The nature and origins of renormalization group ideas in statistical physics and condensed matter theory are recounted informally, emphasizing those features of prime importance in these areas of science in contradistinction to quantum field theory, in particular: critical exponents and scaling, relevance, irrelevance and marginality, universality, and Wilson's crucial concept of flows and fixed points in a large space of Hamiltonians.

Contents

1. Foreword

2. 1 Introduction

3. 2 Whence came renormalization group theory?

4. 3 Where stands the renormalization group?

5. 4 Exponents, anomalous dimensions, scale invariance and scale dependence

6. 5 The challenges posed by critical phenomena

7. 6 Exponent relations, scaling, and irrelevance

8. 7 Relevance, crossover, and marginality

9. 8 The task for renormalization group theory

10. 9 Kadanoff's scaling picture

11. 10 Wilson's quest

12. 11 The construction of renormalization group transformations: the epsilon expansion

13. 12 Flows, fixed points, universality and scaling

14. 13 Conclusions

15. Acknowledgments

16. Selected bibliography

17. Appendix A Asymptotic behavior

18. Appendix B Unitarity of the renormalization group

19. Appendix C Nature of a semigroup

Foreword

It was a pleasure to participate in the Colloquium cosponsored by the Departments of Philosophy and of Physics at Boston University “On the Foundations of Quantum Field Theory.” In the full title, this was preceded by the phrase: “A Historical Examination and Philosophical Reflections,” which set the aims of the meeting. Naturally, the participants were mainly high-energy physicists, experts in field theories, and interested philosophers of science.