Quantum field theory. Lectures of Sidney Coleman. With a foreword by David Kaiser. Edited by Bryan Gin-ge Chen, David Derbes, David Griffiths, Brian Hill, Richard Sohn and Yuan-Sen Ting.

*(English)*Zbl 1431.81001
Hackensack, NJ: World Scientific (ISBN 978-981-4632-53-9/hbk; 978-981-4635-50-9/pbk; 978-981-4635-52-3/ebook). xli, 1152 p. (2019).

Professor Sidney Coleman is well known for the clarity and deepness of his theoretical physics lectures. Several generations of theoretical physicists have profited from his beautiful Erice Lectures on new developments in theoretical high energy physics.

The present book on Quantum Field Theory is one of the best presentations of the subject. The textbooks on Quantum Field Theory are many and most of them follow a rather standard pattern, focused more on the pragmatic effectiveness of its perturbative version than on the conceptual basis of its foundations. The widespread choice of providing a simple account of the theory often leaves open conceptual problems and questions of mathematical consistency.

The praiseworthy merit of Coleman’s book is the attention to the general structure with arguments and derivations always clear and mathematically well founded.

Some of the topics discussed in the book were already presented in various Erice Lectures, but their inclusion in a coherent comprehensive treatment of Quantum Field Theory is very profitable.

The presentation reproduces the major steps of development of Quantum Field Theory and Elementary Particle Theory with an accurate discussion of the conceptual roots of the achievements reached by the theory. The first six Chapters offer a well reasoned account of free fields and their symmetries. Chapters 7–10 give a very clear account of the structure of perturbation theory and of the need of counterterms; the discussion of Models 1, 2, 3, provides concrete and illuminating realizations of the general theory, allowing to better grasp the rules of the game.

Scattering theory is discussed both perturbatively, in terms of Feynman diagrams, and non-perturbatively, in terms of asymptotic limits and LSZ formulas, (Chapters 10–16). Fields describing relativistic particles with spin (in particular Dirac fermions and vector bosons) are presented in Chapters 17–22, 26, underlining the associated symmetries (Lorentz, parity, CPT).

The full renormalization theory with the primary application to Quantum Elecrodynamics is treated in Chapters 23, 25, 27–35. Praiseworthy is the discussion of various approaches, including the BPHZ algorithm and the functional integral formulation. It is hard to find such a clear and well founded account of this topics in the quantum field theory textbooks.

The final part of the book is devoted to the Standard Model of elementary particles, starting from a detailed analysis of Gell-Mann and Ne’eman \(SU(3)\); the next step is current algebra and quark model and the final formulation obtained through the mechanism of spontaneous symmetry breaking in Yang-Mills theories. The origin and establishment of the Glashow-Salam-Weinberg model is discussed in Chapters 48, 49.

One of the great merit of the book is the inclusion of very instructive problems with solutions on the topic developed in the preceding chapters.

The Foreword by David Kaiser gives a nice review of the historical development of Quantum Field Theory of Elementary Particles, with a very detailed bibliography, with comments on Coleman approach to the evolving theory; the Foreword also gives a vivid and lively picture of Coleman character.

The present book on Quantum Field Theory is one of the best presentations of the subject. The textbooks on Quantum Field Theory are many and most of them follow a rather standard pattern, focused more on the pragmatic effectiveness of its perturbative version than on the conceptual basis of its foundations. The widespread choice of providing a simple account of the theory often leaves open conceptual problems and questions of mathematical consistency.

The praiseworthy merit of Coleman’s book is the attention to the general structure with arguments and derivations always clear and mathematically well founded.

Some of the topics discussed in the book were already presented in various Erice Lectures, but their inclusion in a coherent comprehensive treatment of Quantum Field Theory is very profitable.

The presentation reproduces the major steps of development of Quantum Field Theory and Elementary Particle Theory with an accurate discussion of the conceptual roots of the achievements reached by the theory. The first six Chapters offer a well reasoned account of free fields and their symmetries. Chapters 7–10 give a very clear account of the structure of perturbation theory and of the need of counterterms; the discussion of Models 1, 2, 3, provides concrete and illuminating realizations of the general theory, allowing to better grasp the rules of the game.

Scattering theory is discussed both perturbatively, in terms of Feynman diagrams, and non-perturbatively, in terms of asymptotic limits and LSZ formulas, (Chapters 10–16). Fields describing relativistic particles with spin (in particular Dirac fermions and vector bosons) are presented in Chapters 17–22, 26, underlining the associated symmetries (Lorentz, parity, CPT).

The full renormalization theory with the primary application to Quantum Elecrodynamics is treated in Chapters 23, 25, 27–35. Praiseworthy is the discussion of various approaches, including the BPHZ algorithm and the functional integral formulation. It is hard to find such a clear and well founded account of this topics in the quantum field theory textbooks.

The final part of the book is devoted to the Standard Model of elementary particles, starting from a detailed analysis of Gell-Mann and Ne’eman \(SU(3)\); the next step is current algebra and quark model and the final formulation obtained through the mechanism of spontaneous symmetry breaking in Yang-Mills theories. The origin and establishment of the Glashow-Salam-Weinberg model is discussed in Chapters 48, 49.

One of the great merit of the book is the inclusion of very instructive problems with solutions on the topic developed in the preceding chapters.

The Foreword by David Kaiser gives a nice review of the historical development of Quantum Field Theory of Elementary Particles, with a very detailed bibliography, with comments on Coleman approach to the evolving theory; the Foreword also gives a vivid and lively picture of Coleman character.

Reviewer: Franco Strocchi (Pisa)

##### MSC:

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

81Txx | Quantum field theory; related classical field theories |

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

81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |

81T45 | Topological field theories in quantum mechanics |

81R40 | Symmetry breaking in quantum theory |

81U05 | \(2\)-body potential quantum scattering theory |

81T18 | Feynman diagrams |

81V10 | Electromagnetic interaction; quantum electrodynamics |

81V22 | Unified quantum theories |

00A79 | Physics (Use more specific entries from Sections 70-XX through 86-XX when possible) |

00B60 | Collections of reprinted articles |