The Casimir effect : physical manifestations of zero-point energy / K.A. Milton.

Format:

Book

Author/Creator:

Milton, K. A.

Language:

English

Subjects (All):

Casimir effect.

Physical Description:

xv, 301 pages : illustrations ; 23 cm

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, [2001]

Summary:

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.

Contents:

1.1 Van der Waals Forces 1

1.2 Casimir Effect 3

1.3 Dimensional Dependence 8

1.4 Applications 11

1.5 Local Effects 13

1.6 Sonoluminescence 14

1.7 Radiative Corrections 15

1.8 Other Topics 16

Chapter 2 Casimir Force Between Parallel Plates 19

2.2 Dimensional Regularization 20

2.3 Scalar Green's Function 22

2.4 Massive Scalar 28

2.5 Finite Temperature 30

2.6 Electromagnetic Casimir Force 36

2.6.1 Variations 40

2.7 Fermionic Casimir Force 41

2.7.1 Summing Modes 42

2.7.2 Green's Function Method 44

Chapter 3 Casimir Force Between Parallel Dielectrics 49

3.1 The Lifshitz Theory 49

3.2 Applications 53

3.2.1 Temperature Dependence for Conducting Plates 54

3.2.2 Finite Conductivity 57

3.2.3 van der Waals Forces 57

3.2.4 Force between Polarizable Molecule and a Dielectric Plate 59

3.3 Experimental Verification of the Casimir Effect 61

Chapter 4 Casimir Effect with Perfect Spherical Boundaries 65

4.1 Electromagnetic Casimir Self-Stress on a Spherical Shell 65

4.1.1 Temperature Dependence 73

4.2 Fermion Fluctuations 75

Chapter 5 The Casimir Effect of a Dielectric Ball: The Equivalence of the Casimir Effect and van der Waals Forces 79

5.1 Green's Dyadic Formulation 79

5.2 Stress on the Sphere 82

5.3 Total Energy 84

5.4 Fresnel Drag 86

5.5 Electrostriction 88

5.6 Dilute Dielectric-Diamagnetic Sphere 89

5.6.1 Temperature Dependence 92

5.7 Dilute Dielectric Ball 93

5.7.1 Temperature Dependence 96

5.8 Conducting Ball 97

5.9 Van der Waals Self-Stress for a Dilute Dielectric Sphere 99

Chapter 6 Application to Hadronic Physics: Zero-Point Energy in the Bag Model 105

6.1 Zero-point Energy of Confined Gluons 107

6.2 Zero-point Energy of Confined Virtual Quarks 112

6.2.1 Numerical Evaluation 113

6.2.1.1 J = 1/2 Contribution 113

6.2.1.2 Sum Over All Modes 114

6.2.1.3 Asymptotic Evaluation of Lowest J Contributions 115

6.3 Discussion and Applications 116

6.3.1 Fits to Hadron Masses 118

6.4 Calculation of the Bag Constant 120

6.5 Recent Work 123

Chapter 7 Casimir Effect in Cylindrical Geometries 125

7.1 Conducting Circular Cylinder 125

7.1.1 Related Work 132

7.1.2 Parallelepipeds 133

7.1.3 Wedge-Shaped Regions 133

7.2 Dielectric-Diamagnetic Cylinder

Uniform Speed of Light 134

7.2.1 Integral Representation for the Casimir Energy 135

7.2.2 Casimir Energy of an Infinite Cylinder when [epsilon subscript 1 mu subscript 1] = [epsilon subscript 2 mu subscript 2] 137

7.2.3 Dilute Compact Cylinder and Perfectly Conducting Cylindrical Shell 142

7.3 Van der Waals Energy of a Dielectric Cylinder 146

Chapter 8 Casimir Effect in Two Dimensions: The Maxwell-Chern-Simons Casimir Effect 149

8.2 Casimir Effect in 2 + 1 Dimensions 151

8.2.1 Temperature Effect 158

8.2.3 Casimir Force between Chern-Simons Surfaces 159

8.3 Circular Boundary Conditions 160

8.3.1 Casimir Self-Stress on a Circle 161

8.3.2 Numerical Results at Zero Temperature 171

8.3.3 High-Temperature Limit 175

8.4 Scalar Casimir Effect on a Circle 179

Chapter 9 Casimir Effect on a D-dimensional Sphere 183

9.1 Scalar or TE Modes 183

9.2 TM Modes 190

9.2.1 Energy Derivation 193

9.2.2 Numerical Evaluation of the Stress 194

9.2.2.1 Convergent Reformulation of (9.52) 195

9.2.3 Casimir Stress for Integer D [less than or equal] 1 197

9.2.4 Numerical results 198

9.3 Toward a Finite D = 2 Casimir Effect 199

Chapter 10 Cosmological Implications of the Casimir Effect 201

10.1 Scalar Casimir Energies in M[superscript 4] X S[superscript N] 202

10.1.1 N = 1 204

10.1.2 The General Odd-N Case 205

10.1.3 The Even-N Case 208

10.1.4 A Simple [xi]-Function Technique 216

10.3 The Cosmological Constant 220

Chapter 11 Local Effects 223

11.1 Parallel Plates 223

11.2 Local Casimir Effect for Wedge Geometry 228

11.4 Quark and Gluon Condensates in the Bag Model 229

11.5 Surface Divergences 236

Chapter 12 Sonoluminescence and the Dynamical Casimir Effect 239

12.2 The Adiabatic Approximation 242

12.3 Discussion of Form of Force on Surface 244

12.4 Bulk Energy 247

12.5 Dynamical Casimir Effect 249

Chapter 13 Radiative Corrections to the Casimir Effect 255

13.1 Formalism for Computing Radiative Corrections 257

13.2 Radiative Corrections for Parallel Conducting Plates 259

13.2.1 Other Work 262

13.3 Radiative Corrections for a Spherical Boundary 262

Appendix A Relation of Contour Integral Method to Green's Function Approach 269

Appendix B Casimir Effect for a Closed String 273

B.1 Open Strings 275.

Notes:

Includes bibliographical references (pages 277-292) and index.

ISBN:

9810243979

OCLC:

49260085