Foreword ........................................................ 1
Introduction .................................................... 3
Chapter 1 Normal mode quantum electrodynamics: the quantum
vacuum and its consequences ..................................... 7
1 Wave-particle duality ........................................ 7
1.1 Light as a particle ..................................... 7
1.2 Light as a wave ......................................... 8
1.3 The photon .............................................. 8
2 Classical electrodynamics in free space ...................... 9
2.1 Normal modes in free space ............................. 11
2.2 Normal modes inside a cuboid cavity .................... 13
2.3 Normal modes: general remarks .......................... 15
2.4 Electromagnetic waves .................................. 16
2.5 Energy of the electromagnetic field .................... 16
3 Normal mode quantum electrodynamics ......................... 18
3.1 Basic elements of quantum theory ....................... 18
3.2 The quantised electromagnetic field .................... 20
3.3 Quantum statistics and Fock states ..................... 21
3.4 Energy of the electromagnetic field .................... 23
3.5 Quantum dynamics of the electromagnetic field .......... 24
4 The quantum vacuum .......................................... 25
4.1 Vacuum fluctuations .................................... 26
4.2 Thermal fluctuations ................................... 27
5 Quantum vacuum effects in free space ........................ 29
5.1 Atom-field interactions ................................ 29
5.2 Lamb shift ............................................. 32
5.3 Spontaneous decay ...................................... 36
5.4 Electron magnetic moment ............................... 38
5.5 Van der Waals potential ................................ 39
6 Quantum vacuum effects near boundaries ...................... 40
6.1 Casimir-Polder potential ............................... 41
6.2 Purcell effect ......................................... 41
6.3 Electron magnetic moment ............................... 42
6.4 Van der Waals potential ................................ 42
7 The Casimir force ........................................... 42
7.1 Perfectly conducting plates ............................ 42
7.2 Conducting and permeable plates ........................ 48
7.3 Thermal effects ........................................ 49
8 The quantum vacuum revisited ................................ 51
8.1 Vacuum energy .......................................... 51
8.2 Changes in vacuum energy ............................... 52
8.3 Virtual photons ........................................ 52
9 Normal mode QED: discussion ................................. 53
9.1 Advantages ............................................. 53
9.2 Limitations ............................................ 54
10 Problems .................................................... 55
11 Bibliography ................................................ 56
Chapter 2 Van der Waals and Casimir-Polder dispersion forces .. 61
12 Introduction ................................................ 61
13 Van der Waals interaction ................................... 64
13.1 Quasistatic analysis ................................... 65
13.2 Electrodynamic analysis ................................ 67
14 Casimir-Polder atom-surface interaction ..................... 87
14.1 Quasistatic analysis ................................... 87
14.2 Electrodynamic analysis ................................ 89
15 A few comments .............................................. 93
16 Non-additivity of dipolar interactions ...................... 97
16.1 Example: non-additivity in atom-surface interaction .... 97
16.2 Multiple scattering as the origin of non-additivity ... 100
17 Problems ................................................... 103
18 Bibliography ............................................... 105
Chapter 3 The Casimir stress in real materials ............... 107
19 Dispersion and dissipation in real media ................... 108
19.1 Dipole model of the optical response .................. 109
19.2 The Kramers-Kronig relations .......................... 110
19.3 Generalised mode decomposition ........................ 113
19.4 Open quantum systems and Langevin equations ........... 115
19.5 Linear fluctuation-dissipation theorem ................ 117
20 The stress tensor in vacuum ................................ 119
21 Lifshitz theory of dispersion forces ....................... 121
21.1 Rytov's theory of fluctuating electromagnetic fields .. 122
21.2 Lifshitz's approach to the Casimir force .............. 122
21.3 Green function approach ............................... 128
21.4 Thermal contribution to Casimir-Lifshitz forces ....... 134
22 Problems ................................................... 136
23 Bibliography ............................................... 137
Chapter 4 Macroscopic QED and vacuum forces ................... 139
24 Preliminary remarks ........................................ 139
25 An introduction to macroscopic QED ......................... 140
25.1 Macroscopic QED in one dimension ...................... 141
25.2 Macroscopic QED in three dimensions ................... 158
26 Vacuum forces between moving bodies ........................ 164
26.1 Moving bodies in ID macroscopic QED ................... 165
26.2 Computing classical forces ............................ 167
26.3 Quantum theory of radiation pressure .................. 170
26.4 The vacuum force ...................................... 173
26.5 A simple case of quantum friction ..................... 175
26.6 Moving bodies in 3D macroscopic QED ................... 178
26.7 Quantum friction between sliding plates ............... 183
27 Problems ................................................... 189
28 Bibliography ............................................... 191
Chapter 5 Measuring Casimir phenomena ...................... 195
29 General experimental considerations ..................... 196
30 Representative experimental results ........................ 197
30.1 Early results ......................................... 198
30.2 Beginning of the "modern Casimir era" ................. 199
30.3 Effect of material properties ......................... 203
30.4 Effects of temperature ................................ 210
30.5 Recent directions ..................................... 212
31 Techniques for measurement ................................. 213
31.1 Minimum detectable interaction ........................ 215
32 Measurement of the interaction ............................. 216
32.1 Static method ......................................... 216
32.2 Dynamic method ........................................ 218
33 Measurement of the separation .............................. 219
34 Calibration of the apparatus ............................... 220
35 Comparison with theory ..................................... 222
36 Problems ................................................... 222
37 Bibliography ............................................... 224
Chapter 6 Casimir forces at the cutting edge ............... 227
38 Experimental issues in Casimir physics ..................... 227
38.1 Drude or plasma? ...................................... 228
38.2 Patch potentials ...................................... 230
39 Theoretical questions in Casimir physics ................... 232
39.1 Repulsive shells and Casimir's electron ............... 232
39.2 Divergence of the Casimir stress ...................... 234
39.3 Maxwell's fisheye and renormalisation ................. 238
39.4 The Casimir effect and cosmology ...................... 241
40 Bibliography ............................................... 244
Further reading ............................................ 247
Appendix: Regularisation techniques ........................... 251
A Point-splitting regularisation .............................. 251
B Dimensional regularisation .................................. 253
C Zeta-function regularisation ................................ 255
Index ......................................................... 257
About the authors ............................................. 263
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