Introduction To The Theory Of Lie Groups Pdf
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The Standard Model
Author: Yuval Grossman
language: en
Publisher: Princeton University Press
Release Date: 2023-09-26
An authoritative, hands-on introduction to the foundational theory and experimental tests of particle physics The Standard Model is an elegant and extremely successful theory that formulates the laws of fundamental interactions among elementary particles. This incisive textbook introduces students to the physics of the Standard Model while providing an essential overview of modern particle physics, with a unique emphasis on symmetry principles as the starting point for constructing models. The Standard Model equips students with an in-depth understanding of this impressively predictive theory and an appreciation of its beauty, and prepares them to interpret future experimental results. Describes symmetry principles of growing complexity, including Abelian symmetries and their application in QED, the theory of electromagnetic interactions, non-Abelian symmetries and their application in QCD, the theory of strong interactions, and spontaneously broken symmetries and their application in the theory of weak interactions Derives the Lagrangian that implements these symmetry principles and extracts the phenomenology that follows from it, such as elementary particles and accidental symmetries Explains how the Standard Model has been experimentally tested, emphasizing electroweak precision measurements, flavor-changing neutral current processes, neutrino oscillations, and cosmology Demonstrates how to extend the model to address experimental and observational puzzles, such as neutrino masses, dark matter, and the baryon asymmetry of the universe Features a wealth of problems drawing from the latest research Ideal for a one-semester graduate course and an invaluable resource for practitioners Online solutions manual (available only to instructors)
Introduction to Differential Geometry
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Lie Groups and Geometric Aspects of Isometric Actions
This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.