Hardback
Series: Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (No. 31)
ISBN: 9780521437523
304 pages
73 b/w illus.
Dimensions: 247 x 174 mm
available from December 2010
Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of
Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional
graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions,
and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all
orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch
Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon mass arises in QCD. Applications are
given to the center vortex picture of confinement, the gauge-invariant treatment of resonant amplitudes, the definition of
non-Abelian effective charges, high-temperature effects, and even supersymmetry. This book is ideal for elementary particle
theorists and graduate students.
Introduction
1. The Pinch Technique at one loop
2. Advanced pinch technique ? still one loop
3. Pinch technique to all orders
4. The pinch technique in the Batalin-Vilkovisky framework
5. The gauge technique
6. Schwinger-Dyson equations in the pinch technique framework
7. Non-perturbative gluon mass and quantum solitons
8. Nexuses, sphalerons, and fractional topological charge
9. A brief summary of d=3 NAGTs
10. The pinch technique for electroweak theory
11. Other applications of the pinch technique
Appendix
Index.
Paperback
ISBN: 9780521187961
Publication date: March 2011
713 pages
Dimensions: 244 x 170 mm
Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This 2006
textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering:
manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and
so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general
theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for
studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and
gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and
engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required
mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.
Introduction
1. The concept of a manifold
2. Vector and tensor fields
3. Mappings of tensors induced by mappings of manifolds
4. Lie derivative
5. Exterior algebra
6. Differential calculus of forms
7. Integral calculus of forms
8. Particular cases and applications of Stoke's Theorem
9. Poincare Lemma and cohomologies
10. Lie Groups - basic facts
11. Differential geometry of Lie Groups
12. Representations of Lie Groups and Lie Algebras
13. Actions of Lie Groups and Lie Algebras on manifolds
14. Hamiltonian mechanics and symplectic manifolds
15. Parallel transport and linear connection on M
16. Field theory and the language of forms
17. Differential geometry on TM and T*M
18. Hamiltonian and Lagrangian equations
19. Linear connection and the frame bundle
20. Connection on a principal G-bundle
21. Gauge theories and connections
22. Spinor fields and Dirac operator
Appendices
Bibliography
Index.
Hardback
ISBN: 9780521196000
424 pages
40 b/w illus. 45 tables
Dimensions: 234 x 156 mm
available from February 2011
The field of machine learning has matured to the point where many sophisticated learning approaches can be applied to
practical applications. Thus it is of critical importance that researchers have the proper tools to evaluate learning
approaches and understand the underlying issues. This book examines various aspects of the evaluation process with an
emphasis on classification algorithms. The authors describe several techniques for classifier performance assessment, error
estimation and resampling, obtaining statistical significance as well as selecting appropriate domains for evaluation. They
also present a unified evaluation framework and highlight how different components of evaluation are both significantly
interrelated and interdependent. The techniques presented in the book are illustrated using R and WEKA, facilitating better
practical insight as well as implementation. Aimed at researchers in the theory and applications of machine learning, this
book offers a solid basis for conducting performance evaluations of algorithms in practical settings.
1. Introduction
2. Machine learning and statistics overview
3. Performance measures I
4. Performance measures II
5. Error estimation
6. Statistical significance testing
7. Data sets and experimental framework
8. Recent developments
9. Conclusion
Appendix A: statistical tables
Appendix B: additional information on the data
Appendix C: two case studies.