This book introduces the quantum theory of gauge fields, with emphasis on four non-perturbative methods which have important applications: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.
This book introduces the quantum theory of gauge fields, with emphasis on four non-perturbative methods which have important applications: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.
Yuri Makeenko received his PhD in theoretical and mathematical physics from the Institute of Theoretical and Experimental Physics (ITEP), Moscow. He has been a staff member at ITEP since 1983, and since 1993 has been a visiting professor at the Niels Bohr Institute, Copenhagen. He has given lecture courses at universities throughout Europe and has published numerous papers and review articles. Professor Makeenko has been working on non-perturbative quantum field theory since 1975. His research has covered four-dimensional conformal field theories and the 1/N-expansion of QCD, where he derived in 1979 an equation presently known as the MakeenköMigdal equation or the 'loop equation', in collaboration with A.A. Migdal. In the early 1980s he explored lattice gauge theories, including the Monte Carlo simulations, and went on to work on matrix models and string theory in the 1990s. His subsequent work has focused on matrix theory and non-commutative gauge theories.
Inhaltsangabe
Preface Part I. Path Integrals: 1. Operator calculus 2. Second quantization 3. Quantum anomalies from path integral 4. Instantons in quantum mechanics Part II. Lattice Gauge Theories: 5. Observables in gauge theories 6. Gauge fields on a lattice 7. Lattice methods 8. Fermions on a lattice 9. Finite temperatures Part III. 1/N Expansion: 10. O(N) vector models 11. Multicolor QCD 12. QCD in loop space 13. Matrix models Part IV. Reduced Models: 14. Eguchi¿Kawai model 15. Twisted reduced models 16. Non-commutative gauge theories.
Preface Part I. Path Integrals: 1. Operator calculus 2. Second quantization 3. Quantum anomalies from path integral 4. Instantons in quantum mechanics Part II. Lattice Gauge Theories: 5. Observables in gauge theories 6. Gauge fields on a lattice 7. Lattice methods 8. Fermions on a lattice 9. Finite temperatures Part III. 1/N Expansion: 10. O(N) vector models 11. Multicolor QCD 12. QCD in loop space 13. Matrix models Part IV. Reduced Models: 14. Eguchi¿Kawai model 15. Twisted reduced models 16. Non-commutative gauge theories.
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