The Formalisms of Quantum Mechanics: An Introduction

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The Formalisms of Quantum Mechanics: An Introduction (Lecture Notes in Physics) by Francois David
2014 | ISBN: 3319105388 | English | 157 pages | PDF | 1 MB

These lecture notes present a concise & introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics & of quantum field theories, their interrelations & their theoretical foundations.

The "st&ard" formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, & the probabilistic interpretation given by the Born rule) on one h&, & the path integral & functional integral representations of probabilities amplitudes on the other, are the st&ard tools used in most applications of quantum theory in physics & chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension & justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics & the "quantum logic" approach. Last but not least, some emphasis will also be put on underst&ing the relation between quantum physics & special relativity through their common roots - causality, locality & reversibility, as well as on the relation between quantum theory, information theory, correlations & measurements, & quantum gravity.

Quantum mechanics is probably the most successful physical theory ever proposed & despite huge experimental & technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science has become an important & very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics & its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged & dominant paradigm of modern physical sciences & technologies while sometimes it is considered a still mysterious & poorly understood theory, waiting for a revolution. This volume, addressing graduate students & seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics.
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