Casimir Effect, The

Physical Manifestations Of Zero-point Energy

By: Kimball A Milton

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Hardcover | 16 October 2001

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320 Pages

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In its simplest manifestation, the Casimir effect is a quantum force of attraction between two parallel uncharged conducting plates. More generally, it refers to the interaction — which may be either attractive or repulsive — between material bodies due to quantum fluctuations in whatever fields are relevant. It is a local version of the van der Waals force between molecules. Its sweep ranges from perhaps its being the origin of the cosmological constant to its being responsible for the confinement of quarks.This monograph develops the theory of such forces, based primarily on physically transparent Green's function techniques, and makes applications from quarks to the cosmos, as well as observable consequences in condensed matter systems. It is aimed at graduate students and researchers in theoretical physics, quantum field theory, and applied mathematics.

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Non-Fiction Science Physics Particle & High-Energy Physics Materials & States of Matter Condensed Matter Physics including Liquid State & Solid State Physics Nuclear Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Booktopia Publisher Services World Scientific Publishing

Preface	p. vii
Introduction to the Casimir Effect	p. 1
Van der Waals Forces	p. 1
Casimir Effect	p. 3
Dimensional Dependence	p. 8
Applications	p. 11
Local Effects	p. 13
Sonoluminescence	p. 14
Radiative Corrections	p. 15
Other Topics	p. 16
Conclusion	p. 16
General References	p. 16
Casimir Force Between Parallel Plates	p. 19
Introduction	p. 19
Dimensional Regularization	p. 20
Scalar Green's Function	p. 22
Massive Scalar	p. 28
Finite Temperature	p. 30
Electromagnetic Casimir Force	p. 36
Variations	p. 40
Fermionic Casimir Force	p. 41
Summing Modes	p. 42
Green's Function Method	p. 44
Casimir Force Between Parallel Dielectrics	p. 49
The Lifshitz Theory	p. 49
Applications	p. 53
Temperature Dependence for Conducting Plates	p. 54
Finite Conductivity	p. 57
van der Waals Forces	p. 57
Force between Polarizable Molecule and a Dielectric Plate	p. 59
Experimental Verification of the Casimir Effect	p. 61
Casimir Effect with Perfect Spherical Boundaries	p. 65
Electromagnetic Casimir Self-Stress on a Spherical Shell	p. 65
Temperature Dependence	p. 73
Fermion Fluctuations	p. 75
The Casimir Effect of a Dielectric Ball: The Equivalence of the Casimir Effect and van der Waals Forces	p. 79
Green's Dyadic Formulation	p. 79
Stress on the Sphere	p. 82
Total Energy	p. 84
Fresnel Drag	p. 86
Electrostriction	p. 88
Dilute Dielectric-Diamagnetic Sphere	p. 89
Temperature Dependence	p. 92
Dilute Dielectric Ball	p. 93
Temperature Dependence	p. 96
Conducting Ball	p. 97
Van der Waals Self-Stress for a Dilute Dielectric Sphere	p. 99
Discussion	p. 102
Application to Hadronic Physics: Zero-Point Energy in the Bag Model	p. 105
Zero-point Energy of Confined Gluons	p. 107
Zero-point Energy of Confined Virtual Quarks	p. 112
Numerical Evaluation	p. 113
J = 1/2 Contribution	p. 113
Sum Over All Modes	p. 114
Asymptotic Evaluation of Lowest J Contributions	p. 115
Discussion and Applications	p. 116
Fits to Hadron Masses	p. 118
Calculation of the Bag Constant	p. 120
Recent Work	p. 123
Casimir Effect in Cylindrical Geometries	p. 125
Conducting Circular Cylinder	p. 125
Related Work	p. 132
Parallelepipeds	p. 133
Wedge-Shaped Regions	p. 133
Dielectric-Diamagnetic Cylinder--Uniform Speed of Light	p. 134
Integral Representation for the Casimir Energy	p. 135
Casimir Energy of an Infinite Cylinder when [epsilon subscript 1 mu subscript 1] = [epsilon subscript 2 mu subscript 2]	p. 137
Dilute Compact Cylinder and Perfectly Conducting Cylindrical Shell	p. 142
Van der Waals Energy of a Dielectric Cylinder	p. 146
Casimir Effect in Two Dimensions: The Maxwell-Chern-Simons Casimir Effect	p. 149
Introduction	p. 149
Casimir Effect in 2 + 1 Dimensions	p. 151
Temperature Effect	p. 158
Discussion	p. 158
Casimir Force between Chern-Simons Surfaces	p. 159
Circular Boundary Conditions	p. 160
Casimir Self-Stress on a Circle	p. 161
Numerical Results at Zero Temperature	p. 171
High-Temperature Limit	p. 175
Discussion	p. 176
Scalar Casimir Effect on a Circle	p. 179
Casimir Effect on a D-dimensional Sphere	p. 183
Scalar or TE Modes	p. 183
TM Modes	p. 190
Energy Derivation	p. 193
Numerical Evaluation of the Stress	p. 194
Convergent Reformulation of (9.52)	p. 195
Casimir Stress for Integer D [less than or equal] 1	p. 197
Numerical results	p. 198
Toward a Finite D = 2 Casimir Effect	p. 199
Cosmological Implications of the Casimir Effect	p. 201
Scalar Casimir Energies in M[superscript 4] X S[superscript N]	p. 202
N = 1	p. 204
The General Odd-N Case	p. 205
The Even-N Case	p. 208
A Simple [xi]-Function Technique	p. 216
Discussion	p. 219
Other Work	p. 219
The Cosmological Constant	p. 220
Local Effects	p. 223
Parallel Plates	p. 223
Local Casimir Effect for Wedge Geometry	p. 228
Other Work	p. 229
Quark and Gluon Condensates in the Bag Model	p. 229
Surface Divergences	p. 236
Sonoluminescence and the Dynamical Casimir Effect	p. 239
Introduction	p. 239
The Adiabatic Approximation	p. 242
Discussion of Form of Force on Surface	p. 244
Bulk Energy	p. 247
Dynamical Casimir Effect	p. 249
Radiative Corrections to the Casimir Effect	p. 255
Formalism for Computing Radiative Corrections	p. 257
Radiative Corrections for Parallel Conducting Plates	p. 259
Other Work	p. 262
Radiative Corrections for a Spherical Boundary	p. 262
Conclusions	p. 263
Conclusions and Outlook	p. 265
Relation of Contour Integral Method to Green's Function Approach	p. 269
Casimir Effect for a Closed String	p. 273
Open Strings	p. 275
Bibliography	p. 277
Index	p. 293
Table of Contents provided by Syndetics. All Rights Reserved.

Casimir Effect, The

Physical Manifestations Of Zero-point Energy

At a Glance

Hardcover

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