Path Integrals and Quantum Anomalies

Erscheinungsjahr 2004
ISBN: 978-0-19-852913-2
Verlag: Oxford University Press

Buch, Englisch, 296 Seiten, Print PDF, Format (B × H): 162 mm x 242 mm, Gewicht: 577 g

The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. In this book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies. No previous knowledge of field theory beyond the advanced undergraduate quantum mechanics is assumed. The book provides the first coherent introductory treatment of the path integral formulation of chiral and Weyl anomalies, with applications to gauge theory in two and four dimensions, conformal field theory and string theory. Explicit and elementary path integral calculations of most of the quantum anomalies covered are given. The conceptual basis of the path integral bosonization in two-dimensional theory, which may have applications to condensed matter theory, for example, is clarified. The book also covers the recent interesting developments in the treatment of fermions and chiral anomalies in lattice gauge theory.

Zielgruppe

Beginning graduate students and researchers in theoretical physics, mathematics, and chemistry, in particular particle physics theory, high energy nuclear theory, condensed matter theory, and string theory.

Autoren/Hrsg.

Fujikawa, Kazuo

Suzuki, Hiroshi

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Naturwissenschaften Physik Quantenphysik Hochenergiephysik
• Naturwissenschaften Physik Quantenphysik Teilchenphysik

Inhaltsverzeichnis

- 1: Genesis of quantum anomalies

- 2: Feynman path integrals and Schwinger's action principle

- 3: Quantum theory of photons and phase operators

- 4: Regularization of field theory and chiral anomalies

- 5: Jacobians in path integrals and quantum anomalies

- 6: Quantum breaking of gauge symmetry

- 7: Weyl anomaly and renormalization group

- 8: Two-dimensional field theory and bosonization

- 9: Index theorem on the lattice and chiral anomalies

- 10: Gravitational anomalies

- 11: Concluding remarks

- A: Basics of quantum electrodynamics

- B: Field theory in curved space-time

- C: References with brief comments

Über Autor(innen)

Prof. Kazuo Fujikawa, Dept of Physics, University of Tokyo, [e-mail]

Prof. Hiroshi Suzuki, Dept of Mathematical Sciences, Ibaraki University, [e-mail]