Geometry, Topology and Quantum Field Theory

ISBN-13: 9789048163380 / Angielski / Miękka / 2011 / 220 str.

P. Bandyopadhyay

Opis

This monograph deals with the geometrical and topological aspects related to quantum field theory with special reference to the electroweak theory and skyrmions. This book is unique in its emphasis on the topological aspects of a fermion manifested through chiral anomaly which is responsible for the generation of mass. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. These geometrical and topological features help us to consider a massive fermion as a skyrmion and for a composite state we can realise the internal symmetry of hadrons from reflection group. Also, an overview of noncommutative geometry has been presented and it is observed that the manifold M 4 x Z2 has its relevance in the description of a massive fermion as skyrmion when the discrete space is considered as the internal space and the symmetry breaking gives rise to chiral anomaly leading to topological features.

Spis treści

1: Theory of Spinors. 1.1. Spinors and Spin Structure. 1.2. Spinors in Different Dimensions. 1.3. Supersymmetry and Superspace. 2: Fermions and Topology. 2.1. Fermi Field and Nonlinear Sigma Model. 2.2. Quantization and Anomaly. 2.3. Anomaly and Topology. 3: Electroweak Theory. 3.1. Weinberg-Salam Theory. 3.2. Topological Features in Field Theory. 3.3. Topological Origin of Mass. 4: Skyrme Model. 4.1. Nonlinear Sigma Model. 4.2. Skyrme Model for Nucleons. 4.3. Baryons as Three Flavor Solitons. 5: Geometrical Aspects of a Skyrmion. 5.1. Microlocal Space Time and Fermions. 5.2. Internal Symmetry of Hadrons. 5.3. Supersymmetry and Internal Symmetry. 6: Noncommutative Geometry. 6.1. Quantum Space Time. 6.2. Noncommutative Geometry and Particle Physics. 6.3. Discrete Space as the Internal Space.