Cover image for On the Emergence Theme of Physics.
On the Emergence Theme of Physics.
Title:
On the Emergence Theme of Physics.
Author:
Carroll, Robert.
ISBN:
9789814291804
Personal Author:
Physical Description:
1 online resource (288 pages)
Contents:
Contents -- Preface -- Chapter 1. SOME QUANTUM BACKGROUND -- 1. deBROGLIE-BOHM MECHANICS -- 1.1. SUBQUANTUM THERMODYNAMICS -- 1.2. FLUCTUATIONS AND FISHER INFORMATION -- 1.3. THE QUANTUM EQUIVALENCE PRINCIPLE - QEP -- 2. ON THE GUTZWILLER TRACE FORMULA -- 2.1. PROPAGATORS, KERNELS, AND THE WIGNER FUNCTION -- 2.2. REMARKS ON THE TRACE FORMULA -- 2.3. COHERENT STATES AND THE TRACE FORMULA -- 2.4. SOME MATHEMATICAL VARIATIONS -- 3. MORE ON METAPLECTIC TECHNIQUES -- Chapter 2. SOME GEOMETRIC ASPECTS -- 1. INTRODUCTION -- 2. REMARKS ON WEYL GEOMETRY -- 3. EMERGENCE OF Q IN GEOMETRY -- 3.1. QUANTUM POTENTIAL AS A DYNAMICAL FIELD -- 4. OTHER GEOMETRIC ASPECTS -- 5. THE QUANTUM POTENTIAL AND GEOMETRY -- 6. CONFORMAL AND QUANTUM MASS -- 7. RICCI FLOW AND THE QUANTUM POTENTIAL -- 7.1. EXPANSION -- 8. REMARKS ON THE FRIEDMAN EQUATIONS -- 9. ENHANCEMENT -- 10. SOME HEURISTIC RESULTS -- Chapter 3. ASPECTS OF EMERGENCE -- 1. INTRODUCTION -- 2. SOME CLASSICAL QUANTUM RELATIONS -- 3. NC FIELDS AND GRAVITY -- 3.1. REVIEW OF SOME IDEAS -- 4. GERBES AND STRUCTURE -- Chapter 4. KALUZA-KLEIN AND COSMOLOGY -- 1. INTRODUCTION -- 2. KALUZA-KLEIN THEORY -- 3. INDUCED MATTER THEORY -- 4. MORE ON ELECTROMAGNETISM -- 5. 5-D PHYSICS -- 6. SOME QUANTUM CONNECTIONS -- 7. REMARKS ON COSMOLOGY -- 8. EXTENSIONS -- 8.1. MORE EXAMPLES -- Chapter 5. REMARKS ON THERMODYNAMICS AND GRAVITY -- 1. INTRODUCTION -- 1.1. INFORMATION DYNAMICS -- 1.2. ENTROPY AND THE EINSTEIN EQUATIONS -- 2. HORIZONS, ENTROPY, AND ALL THAT -- 3. THERMODYNAMICS AND FRW FORMATS -- 3.1. METRICS FROM (1) -- 3.2. METRICS FROM (3) -- 3.3. METRICS FROM (2) -- 4. THE GEOMETRY OF THERMODYNAMICS -- 4.1. UNIFIED LEGENDRE FORMS -- 5. FRW FOLLOWING (4) AND (5) -- 5.1. HIGHER DERIVATIVE GRAVITIES -- 6. THERMODYNAMICS AND QUANTUM GRAVITY - I -- 6.1. THERMODYNAMICS OF THE UNIVERSE.

7. THERMODYNAMICS AND QUANTUM GRAVITY - II -- 7.1. BOSON FIELDS AND QUANTIZATION -- 7.2. FOCK SPACE CONSTRUCTIONS -- 8. THERMODYNAMICS AND QUANTUM GRAVITY - III -- 8.1. QUANTUM COSMOLOGY -- 8.2. PARTIAL SUMMARY -- Chapter 6. GEOMETRY AND MECHANICS -- 1. MORE ON EMERGENCE -- 1.1. FLUCTUATIONS AND DISSIPATION -- 1.2. PREQUANTIZATION AND BORN'S RULE -- 2. QUANTUM MECHANICS, GRAVITY, AND RICCI FLOW -- 3. THERMODYNAMICS, GRAVITY, AND QUANTUM THEORY -- 3.1. GEOMETRIC FLOWS AND ENTROPY -- 4. MORE ON GRAVITATION -- 5. BLACK HOLES AND THERMODYNAMICS -- Chapter 7. ON TIME AND THE UNIVERSE -- 1. TIME -- 2. SPACETIME, MATHEMATICS, AND PHYSICS -- 3. NON-COMMUTATIVE GEOMETRY -- 4. MORE ON FUNDAMENTAL MATTERS -- 4.1. NC GEOMETRY, GRAVITY, AND STRINGS -- 4.2. TIME AND GEOMETRY -- Chapter 8. GRAVITY AND THE QUANTUM POTENTIAL -- 1. INTRODUCTION -- 2. BACKGROUND -- 3. QEP AND GRAVITY -- 3.1. WEYL GEOMETRY AND THE QUANTUM POTENTIAL -- 4. ON THE KLEIN-GORDON EQUATION -- 4.1. ENHANCEMENT -- 5. QUANTIZATION -- Bibliography -- Index.
Abstract:
The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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