Structural aspects of quantum field theory and noncommutative geometry. Vol. 1.

*(English)*Zbl 1275.81002
Hackensack, NJ: World Scientific (ISBN 978-981-4472-69-2/set; 978-981-4472-72-2/hbk). xxxii, 849 p., index 12 p. (2013).

This self-contained, comprehensive first volume presents a fundamental and careful introduction to quantum field theory. It will be welcomed by students as well as researchers, since it gives an overview of the origin and development of the basic ideas of modern particle physics, quantum statistical mechanics and the mathematics behind. It starts with an overview of classical field theory and then discusses the standard model of particle physics, general relativity and super-gravity. To quantize classical fields, the author uses the path integral method and this way treats the self-interacting scalar field model and QED. Quantum chromodynamics and the related concept of asymptotic freedom are also discussed. The last chapter studies quantum field theory at nonzero temperature, the Bose-Einstein condensation, superconductivity, the fractional quantum Hall effect, Chern-Simons theory, and Laughlin’s ground state wave function, and thus the book provides a rich collection of modern research topics and references to important recent published work.

Reviewer: Gert Roepstorff (Aachen)

##### MSC:

81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |

81R60 | Noncommutative geometry in quantum theory |

81T13 | Yang-Mills and other gauge theories in quantum field theory |

81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |

81V05 | Strong interaction, including quantum chromodynamics |

81V10 | Electromagnetic interaction; quantum electrodynamics |

81V22 | Unified quantum theories |

83E50 | Supergravity |