From Classical to Quantum Fields (Paperback)

Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a reference for active researchers in the field.

量子場論已成為大多數現代理論物理學的通用語言。這本入門教材展示了這個美麗的理論如何提供正確的數學框架來描述和理解基本粒子的基本相互作用。該書首先簡要回顧了基本的古典場論、電動力學和廣義相對論，以及它們的對稱性質，然後按照費曼的路徑積分方法介紹了量子化的原則。在每一步中都特別謹慎地說明了基本假設的正確數學表述。詳細討論了規範理論及其量子化遇到的問題。最後幾章包含了粒子物理學的標準模型的完整描述，以及超越標準模型的嘗試，如大統一理論和超對稱性。本書針對物理學和數學的高年級本科生和初級研究生，也可作為該領域活躍研究人員的參考書。