Neumaier A. Algebraic Quantum Physics. Quantum Mechanics via Lie Algebras 2024
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Neumaier A. Algebraic Quantum Physics. Quantum Mechanics via Lie Algebras 2024
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This monograph introduces mathematicians, physicists, and engineers to the ideas relating quantum mechanics and symmetries - both described in terms of Lie algebras and Lie groups. The exposition of quantum mechanics from this point of view reveals that classical mechanics and quantum mechanics are very much alike. Written by a mathematician and a physicist, this book is (like a math book) about precise concepts and exact results in classical mechanics and quantum mechanics, but motivated and discussed (like a physics book) in terms of their physical meaning. The reader can focus on the simplicity and beauty of theoretical physics, without getting lost in a jungle of techniques for estimating or calculating quantities of interest.
Preface
Basic concepts and principles
Introduction
Outline of the book
Continuous and infinitesimal symmetries
Classical mechanics and quantum mechanics
The meaning of quantum mechanics
Introduction
Measurement in quantum mechanics
Quantum dynamics and spectroscopy
On the foundations of quantum mechanics
The symmetries of space and time
Introduction
Rotations and translations
Unitary groups: Few-level systems, qubits, quarks
Lie groups and Lie algebras
Important families of Lie algebras
Symmetries of spacetime
Conservative classical mechanics
Introduction
Classical oscillating systems
Conservative classical mechanics
The dynamics of quantum systems
Introduction
Hamiltonian quantum mechanics
Quantum oscillators and coherent states
Dynamical equations for quantum systems
Representations of groups and Lie algebras
Introduction
Representation theory
Representations for quantum particles
Spectra and spectroscopy
Bibliography
Author index
Symbol index
Subject index