Quantum theory, groups and representations : an introduction /
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Author / Creator: | Woit, Peter, author. |
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Imprint: | Cham, Switzerland : Springer, 2017. |
Description: | 1 online resource (xxii, 668 pages) : illustrations |
Language: | English |
Subject: | |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11454952 |
Table of Contents:
- Preface
- 1 Introduction and Overview
- 2 The Group U(1) and its Representations
- 3 Two-state Systems and SU(2)
- 4 Linear Algebra Review, Unitary and Orthogonal Groups
- 5 Lie Algebras and Lie Algebra Representations
- 6 The Rotation and Spin Groups in 3 and 4 Dimensions
- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field
- 8 Representations of SU(2) and SO(3)
- 9 Tensor Products, Entanglement, and Addition of Spin
- 10 Momentum and the Free Particle
- 11 Fourier Analysis and the Free Particle
- 12 Position and the Free Particle
- 13 The Heisenberg group and the Schrödinger Representation
- 14 The Poisson Bracket and Symplectic Geometry
- 15 Hamiltonian Vector Fields and the Moment Map
- 16 Quadratic Polynomials and the Symplectic Group
- 17 Quantization
- 18 Semi-direct Products.- 19 The Quantum Free Particle as a Representation of the Euclidean Group
- 20 Representations of Semi-direct Products
- 21 Central Potentials and the Hydrogen Atom
- 22 The Harmonic Oscillator
- 23 Coherent States and the Propagator for the Harmonic Oscillator
- 24 The Metaplectic Representation and Annihilation and Creation Operators, d = 1
- 25 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d
- 26 Complex Structures and Quantization
- 27 The Fermionic Oscillator
- 28 Weyl and Clifford Algebras
- 29 Clifford Algebras and Geometry
- 30 Anticommuting Variables and Pseudo-classical Mechanics
- 31 Fermionic Quantization and Spinors
- 32 A Summary: Parallels Between Bosonic and Fermionic Quantization
- 33 Supersymmetry, Some Simple Examples
- 34 The Pauli Equation and the Dirac Operator
- 35 Lagrangian Methods and the Path Integral
- 36 Multi-particle Systems: Momentum Space Description
- 37 Multi-particle Systems and Field Quantization
- 38 Symmetries and Non-relativistic Quantum Fields
- 39 Quantization of Infinite dimensional Phase Spaces
- 40 Minkowski Space and the Lorentz Group
- 41 Representations of the Lorentz Group
- 42 The Poincaré Group and its Representations
- 43 The Klein-Gordon Equation and Scalar Quantum Fields
- 44 Symmetries and Relativistic Scalar Quantum Fields
- 45 U(1) Gauge Symmetry and Electromagnetic Field
- 46 Quantization of the Electromagnetic Field: the Photon
- 47 The Dirac Equation and Spin-1/2 Fields
- 48 An Introduction to the Standard Model
- 49 Further Topics
- A Conventions
- B Exercises
- Index.