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

Textbook in PDF format 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