Book contents
- Uncovering Quantum Field Theory and the Standard Model
- Reviews
- Uncovering Quantum Field Theory and the Standard Model
- Copyright page
- Contents
- Preface
- Part I Quantum Field Theory
- Part II Construction of The Standard Model
- Part III Strong Interaction
- 18 Quantum Chromodynamics
- 19 Topology of Gauge Fields
- 20 U(1)A-Problem
- 21 Spectrum of Light Baryons andMesons
- 22 Partons and Hard Processes
- 23 Chiral Perturbation Theory
- 24 Topology of Nambu–Goldstone Boson Fields
- Part IV Selected Topics beyond the Standard Model
- Book part
- References
- Author Index
- Subject Index
19 - Topology of Gauge Fields
from Part III - Strong Interaction
Published online by Cambridge University Press: 06 February 2025
Book contents
- Uncovering Quantum Field Theory and the Standard Model
- Reviews
- Uncovering Quantum Field Theory and the Standard Model
- Copyright page
- Contents
- Preface
- Part I Quantum Field Theory
- Part II Construction of The Standard Model
- Part III Strong Interaction
- 18 Quantum Chromodynamics
- 19 Topology of Gauge Fields
- 20 U(1)A-Problem
- 21 Spectrum of Light Baryons andMesons
- 22 Partons and Hard Processes
- 23 Chiral Perturbation Theory
- 24 Topology of Nambu–Goldstone Boson Fields
- Part IV Selected Topics beyond the Standard Model
- Book part
- References
- Author Index
- Subject Index
Summary
The topological charge of smooth Yang–Mills gauge fields is discussed, describing in particular the SU(2) instanton. This leads to the Adler–Bell–Jackiw anomaly and to θ-vacuum states, which are similar to energy bands in a crystal. We finally discuss the Atiyah–Singer index theorem in the continuum and more explicitly on the lattice.
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- Uncovering Quantum Field Theory and the Standard Model , pp. 417 - 441Publisher: Cambridge University PressPrint publication year: 2025