Quantum potential: physics, geometry and algebra
Bohm's realist interpretation of quantum mechanics is an important alternative to Copenhagen interpretation. Although Bohm's theory never was the mainstream, nevertheless it is enjoying a steady development in different directions. It may be difficult for a newcomer to trace all important advances done since Bohm's original texts. The ``brief in physics'' under review would be extremely useful for this task. It is not intended to be an introduction into Bohm's theory, some understanding is required in advance. This permits to provide a condensed presentation of the current state of art with the extensive lists of references to important works, provided at the end of each chapter. The following table of contents gives a good overview of covered topics. \textbf{1 A Short Survey on a ``Strange'' Potential} \quad 1.1 From de Broglie's Pilot Wave to Bohm's Quantum Potential \quad 1.2 The Dynamic and Geometric Approaches to the Quantum Potential \qquad 1.2.1 The Quantum Trajectories of Dürr, Goldstein, Tumulka and Zanghì \qquad 1.2.2 The Quasi-Newtonian Quantum Potential. \qquad 1.2.3 The Thermodynamic Way to the Quantum Potential \qquad 1.2.4 The Geometrodynamic Approach to the Quantum Potential \qquad 1.2.5 The Entropic Approach to Quantum Potential \quad 1.3 Non-commutative Quantum Geometry and Hiley's Algebra Processes in Pre-space \quad References \textbf{2 The Quantum Potential in Particle and Field Theory Models} \quad 2.1 A Bohmian Way to the Klein--Gordon Relativistic Wave Equation \quad 2.2 The Quantum Potential in Dirac Relativistic Quantum Mechanics \quad 2.3 The Quantum Potential in Relativistic Quantum Field Theory \quad References \textbf{3 The Quantum Potential in Gravity and Cosmology} \quad 3.1 Bohm Theory in Curved Space-Time \quad 3.2 Bohmian Theories on Quantum Gravity \quad 3.3 The Role of Quantum Potential in Cosmology \quad References \textbf{4 Entropy, Information, Chaos and the Quantum Potential} \quad 4.1 A Short Survey About the Approaches to Quantum Entropy and Quantum Information \qquad 4.1.1 Von Neumann Entropy and Shannon Information \qquad 4.1.2 Kak's Approach to Quantum Information \qquad 4.1.3 Sbitnev's Approach to Quantum Entropy \qquad 4.1.4 Quantum Entropy, Fisher Information and the Quantum Potential \quad 4.2 Chaos and the Quantum Potential \quad References.
scientific article; zbMATH DE number 6176776