Witten Index

This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by students in advanced undergraduate quantum mechanics courses. Problems have been given at the end of each chapter, along with complete solutions to all the problems. The text also includes material of interest in current research not usually discussed in traditional courses on quantum mechanics, such as the connection between exact solutions to classical solution problems and isospectral quantum Hamiltonians, and the relation to the inverse scattering problem.

These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.

This 2015 advanced textbook, now OA, provides students with a unified understanding of all matter at a fundamental level.

This book describes the basic concepts of supersymmetric theories. It is aimed at theorists, experimentalists and cosmologists interested in supersymmetry, and its content is correspondingly divided into three distinct tracks of study. The topics covered include a discussion of the motivation for supersymmetry in fundamental physics, a description of the minimal supersymmetric model as well as models of grand unification and string models, a presentation of the main scenarios forsupersymmetry breaking, including the concepts and results of dynamical breaking. On the astrophysics/cosmology side, the book includes discussions of supersymmetric dark matter candidates, inflation, dark energy, and the cosmological constant problem. Some very basic knowledge of quantum field theoryis needed and extensive appendices (in particular an introduction to the Standard Model of fundamental interactions) allow the reader to refresh and complete their notions.

A pedagogical and self-contained discussion on monolayer and bilayer quantum Hall systems is given in this volume in a field-theoretical framework, with an introduction to quantum field theory, anyon physics and Chem-Simons gauge theory.

Since the advent of Yang–Mills theories and supersymmetry in the 1970s, quantum field theory - the basis of the modern description of physical phenomena at the fundamental level - has undergone revolutionary developments. This is the first systematic and comprehensive text devoted specifically to modern field theory, bringing readers to the cutting edge of current research. The book emphasizes nonperturbative phenomena and supersymmetry. It includes a thorough discussion of various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective. Featuring extensive cross-referencing from traditional topics to recent breakthroughs in the field, it prepares students for independent research. The side boxes summarizing the main results and over 70 exercises make this an indispensable book for graduate students and researchers in theoretical physics.

The book is based on lectures given at the TASI summer school of 2010. It aims to provide advanced graduate students, postdoctorates and senior researchers with a survey of important topics in particle physics and string theory, with special emphasis on applications of methods from string theory and quantum gravity in condensed matter physics and QCD (especially heavy ion physics). Contents: Overview:Introduction to Gauge/Gravity Duality (J Polchinski)TASI Lectures on Holographic Space-Time, SUSY, and Gravitational Effective Field Theory (T Banks)LHC Physics:Fundamentals of LHC Experiments (J Nielsen)Theoretical Particle Physics at Hadron Colliders: An Introduction (M J Strassler)String Model Building, Landscape and Phenomenology:TASI Lectures: Particle Physics from Perturbative and Non-perturbative Effects in D-Braneworlds (M Cvetic and J Halverson)Supergravity and String Vacua in Various Dimensions (W Taylor)TASI Lectures on Complex Structures (F Denef)Supersymmetry from the Top Down (M Dine)AdS/CFT Applications:The Landscape of the Hubbard Model (S Sachdev)Holography for Strongly Coupled Media (D T Son)Collisions in Anti-de Sitter Space, Conformal Symmetry, and Holographic Superconductors (S S Gubser)Emergence of Supersymmetry, Gauge Theory and String Theory in Condensed Matter Systems (S-S Lee)Lectures on Holographic Non-Fermi Liquids and Quantum Phase Transitions (N Iqbal, H Liu and M Mezei)The Fluid/Gravity Correspondence (S Minwalla, V E Hubeny and M Rangamani) Readership: Graduate students, beginning post-docs and advanced researchers. Keywords:String Theory;condensed Matter Physics;Heavy Ion Physics;AdS-CFT Correspondence