Title Quantum potential : physics, geometry and algebra / Ignazio Licata, Davide Fiscaletti

Published Cham : Springer, 2014

Table of Contents
1.	A Short Survey on a "Strange" Potential					1
1.1.	From de Broglie's Pilot Wave to Bohm's Quantum Potential					1
1.2.	The Dynamic and Geometric Approaches to the Quantum Potential					8
1.2.1.	The Quantum Trajectories of Durr, Goldstein, Tumulka and Zanghi					8
1.2.2.	The Quasi-Newtonian Quantum Potential					13
1.2.3.	The Thermodynamic Way to the Quantum Potential					18
1.2.4.	The Geometrodynamic Approach to the Quantum Potential					27
1.2.5.	The Entropic Approach to Quantum Potential					29
1.3.	Non-commutative Quantum Geometry and Hiley's Algebra Processes in Pre-space					36
	References					45
2.	The Quantum Potential in Particle and Field Theory Models					49
2.1.	A Bohmian Way to the Klein-Gordon Relativistic Wave Equation					49
2.2.	The Quantum Potential in Dirac Relativistic Quantum Mechanics					55
2.3.	The Quantum Potential in Relativistic Quantum Field Theory					59
	References					66
3.	The Quantum Potential in Gravity and Cosmology					69
3.1.	Bohm Theory in Curved Space-Time					69
3.2.	Bohmian Theories on Quantum Gravity					71
3.3.	The Role of Quantum Potential in Cosmology					79
	References					89
4.	Entropy, Information, Chaos and the Quantum Potential					93
4.1.	A Short Survey About the Approaches to Quantum Entropy and Quantum Information					93
4.1.1.	Von Neumann Entropy and Shannon Information					93
4.1.2.	Kak's Approach to Quantum Information					94
4.1.3.	Sbitnev's Approach to Quantum Entropy					96
4.1.4.	Quantum Entropy, Fisher Information and the Quantum Potential					98
4.2.	Chaos and the Quantum Potential					101
	References					105

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Description 1 online resource (xiv, 106 pages) Series SpringerBriefs in Physics, 2191-5423 SpringerBriefs in physics, 2191-5423 Contents From the Contents: Quantum Potential -- The Quantum Potential in Schrödinger Equation -- The Pilot Wave Theory -- Particles' trajectories as the foundation of Bohm's mechanics: the nutshell of Dürr, Goldstein, Tumulka and Zanghì -- Non-Commutative Quantum Geometry and the Algebraic Approach to Non-Locality -- Quantum potential in particle and field theory models -- Klein Gordon Equation and Bertoldi-Faraggi-Matone Theory -- The quantum potential in Bohm's approach to the Dirac relativistic quantum mechanics -- Quantum Potential in Curved Space Field Theory Summary Recently the interest in Bohm realist interpretation of quantum mechanics has grown. The important advantage of this approach lies in the possibility to introduce non-locality ab initio, and not as an "unexpected host". In this book the authors give a detailed analysis of quantum potential, the non-locality term and its role in quantum cosmology and information. The different approaches to the quantum potential are analysed, starting from the original attempt to introduce a realism of particles trajectories (influenced by de Broglie's pilot wave) to the recent dynamic interpretation provided by Goldstein, Durr, Tumulka and Zangh, and the geometrodynamic picture, with suggestion about quantum gravity. Finally we focus on the algebraic reading of Hiley and Birkbeck school, that analyse the meaning of the non-local structure of the world, bringing important consequences for the space, time and information concepts Bibliography Includes bibliographical references Notes Online resource; title from PDF title page (SpringerLink, viewed November 25, 2013) Subject Quantum theory -- Mathematics SCIENCE -- Energy. SCIENCE -- Mechanics -- General. SCIENCE -- Physics -- General. Physique. Astronomie. Quantum theory -- Mathematics Form Electronic book Author Fiscaletti, Davide, author ISBN 9783319003337 331900333X 3319003321 9783319003320

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