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商品描述
This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories.
The book is targeted to researchers and graduate students.
商品描述(中文翻譯)
這本書提供了量子場論中異常現象的現代觀點。全書分為六個部分。第一部分為準備性內容，涵蓋了費米子（fermions）的介紹、古典對稱性（classical symmetries）的描述，以及對共形對稱性（conformal symmetry）的簡短介紹。第二部分專注於異常現象（anomalies）與上同調（cohomology）之間的關係。第三部分探討了計算規範（gauge）、微分同構（diffeomorphism）和跡異常（trace anomalies）的微擾方法（perturbative methods）。在第四部分，使用非微擾的熱核類似方法（non-perturbative heat-kernel-like methods）計算相同的異常現象。第五部分專注於家族指數定理（family's index theorem）及其在手徵異常（chiral anomalies）中的應用，以及微分特徵（differential characters）及其在全局異常（global anomalies）中的應用。第六部分則專注於特殊主題，包括在二維MAT背景下對Dirac費米子跡異常和微分同構異常的完整計算、場論中的Wess-Zumino項、σ模型（sigma models）、它們的局部和全局異常及其抵消，最後分析弦理論和超弦理論的世界面（worldsheet）、σ模型和目標空間異常。
本書的目標讀者為研究人員和研究生。
作者簡介
Loriano Bonora has been Professor of Field Theory at the International School for Advanced Studies (SISSA), Trieste, Italy.
作者簡介(中文翻譯)
洛里亞諾·博諾拉（Loriano Bonora）曾擔任義大利的國際高等研究學院（SISSA）場論教授。
