Search Results - "Lie algebra"

Quantum theory for mathematicians by Hall, Brian C.

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A first course in the sporadic SICs by Stacey, Blake C.

Contents: “…Equiangular Lines -- Sporadic SICs and the Exceptional Lie Algebras -- The Hoggar-type SICs.-SICs as Equicoherent Quantum States -- SICs and Bell Inequalities.…”
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Operational quantum theory by Saller, Heinrich

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Quantum theory, groups and representations : an introduction by Woit, Peter

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.…”
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