Introduction to Quantum Fields on a Lattice

This book provides a concise introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as 'triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-Abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.

這本書提供了對格點上的量子場的簡明介紹：通過將連續的時空替換為格點上的一組離散點，獲得了量子場理論的精確且非摄动的定義。使用弱耦合和強耦合展開，通過具體的例子解釋了格點上的路徑積分。描述了基本概念，如希格斯場的“平凡性”以及夸克和膠子被束縛成強子的情況，并通過數值模擬的結果進行了說明。本書還介紹了手徵對稱性和手徵規範理論，以及量子化的非阿貝爾規範場、尺度和普遍性。本書基於作者的講義，包含了許多解釋性的例子和練習題，適合作為高年級本科生和研究生課程的教材。該書最初於2002年出版，現已重新發行為劍橋核心的開放存取出版物。