The Casimir Effect: Physical Manifestations of Zero-Point Energy

by Milton, Kimball A.

• ISBN13: 9789810243975
• ISBN10: 9810243979
• Format: Hardcover
• Copyright: 2001-12-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Monograph develops the theory of quantum 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.

Table of Contents

Preface	vii
Introduction to the Casimir Effect	1	(18)
Van der Waals Forces	1	(2)
Casimir Effect	3	(5)
Dimensional Dependence	8	(3)
Applications	11	(2)
Local Effects	13	(1)
Sonoluminescence	14	(1)
Radiative Corrections	15	(1)
Other Topics	16	(1)
Conclusion	16	(1)
General References	16	(3)
Casimir Force Between Parallel Plates	19	(30)
Introduction	19	(1)
Dimensional Regularization	20	(2)
Scalar Green's Function	22	(6)
Massive Scalar	28	(2)
Finite Temperature	30	(6)
Electromagnetic Casimir Force	36	(5)
Variations	40	(1)
Fermionic Casimir Force	41	(8)
Summing Modes	42	(2)
Green's Function Method	44	(5)
Casimir Force Between Parallel Dielectrics	49	(16)
The Lifshitz Theory	49	(4)
Applications	53	(8)
Temperature Dependence for Conducting Plates	54	(3)
Finite Conductivity	57	(1)
van der Waals Forces	57	(2)
Force between Polarizable Molecule and a Dielectric Plate	59	(2)
Experimental Verification of the Casimir Effect	61	(4)
Casimir Effect with Perfect Spherical Boundaries	65	(14)
Electromagnetic Casimir Self-Stress on a Spherical Shell	65	(10)
Temperature Dependence	73	(2)
Fermion Fluctuations	75	(4)
The Casimir Effect of a Dielectric Ball: The Equivalence of the Casimir Effect and van der Waals Forces	79	(26)
Green's Dyadic Formulation	79	(3)
Stress on the Sphere	82	(2)
Total Energy	84	(2)
Fresnel Drag	86	(2)
Electrostriction	88	(1)
Dilute Dielectric-Diamagnetic Sphere	89	(4)
Temperature Dependence	92	(1)
Dilute Dielectric Ball	93	(4)
Temperature Dependence	96	(1)
Conducting Ball	97	(2)
Van der Waals Self-Stress for a Dilute Dielectric Sphere	99	(3)
Discussion	102	(3)
Application to Hadronic Physics: Zero-Point Energy in the Bag Model	105	(20)
Zero-point Energy of Confined Gluons	107	(5)
Zero-point Energy of Confined Virtual Quarks	112	(4)
Numerical Evaluation	113	(1)
J = 1/2 Contribution	113	(1)
Sum Over All Modes	114	(1)
Asymptotic Evaluation of Lowest J Contributions	115	(1)
Discussion and Applications	116	(4)
Fits to Hadron Masses	118	(2)
Calculation of the Bag Constant	120	(3)
Recent Work	123	(2)
Casimir Effect in Cylindrical Geometries	125	(24)
Conducting Circular Cylinder	125	(9)
Related Work	132	(1)
Parallelepipeds	133	(1)
Wedge-Shaped Regions	133	(1)
Dielectric-Diamagnetic Cylinder - Uniform Speed of Light	134	(12)
Integral Representation for the Casimir Energy	135	(2)
Casimir Energy of an Infinite Cylinder when ∈1μ1 = ∈2μ2	137	(5)
Dilute Compact Cylinder and Perfectly Conducting Cylindrical Shell	142	(4)
Van der Waals Energy of a Dielectric Cylinder	146	(3)
Casimir Effect in Two Dimensions: The Maxwell-Chern-Simons Casimir Effect	149	(34)
Introduction	149	(2)
Casimir Effect in 2 + 1 Dimensions	151	(9)
Temperature Effect	158	(1)
Discussion	158	(1)
Casimir Force between Chern-Simons Surfaces	159	(1)
Circular Boundary Conditions	160	(19)
Casimir Self-Stress on a Circle	161	(10)
Numerical Results at Zero Temperature	171	(4)
High-Temperature Limit	175	(1)
Discussion	176	(3)
Scalar Casimir Effect on a Circle	179	(4)
Casimir Effect on a D-dimensional Sphere	183	(18)
Scalar or TE Modes	183	(7)
TM Modes	190	(9)
Energy Derivation	193	(1)
Numerical Evaluation of the Stress	194	(1)
Convergent Reformulation of (9.52)	195	(2)
Casimir Stress for Integer D ≤ 1	197	(1)
Numerical results	198	(1)
Toward a Finite D = 2 Casimir Effect	199	(2)
Cosmological Implications of the Casimir Effect	201	(22)
Scalar Casimir Energies in M4 x SN	202	(17)
N = 1	204	(1)
The General Odd-N Case	205	(3)
The Even-N Case	208	(8)
A Simple ζ-Function Technique	216	(3)
Discussion	219	(1)
Other Work	219	(1)
The Cosmological Constant	220	(3)
Local Effects	223	(16)
Parallel Plates	223	(5)
Local Casimir Effect for Wedge Geometry	228	(1)
Other Work	229	(1)
Quark and Gluon Condensates in the Bag Model	229	(7)
Surface Divergences	236	(3)
Sonoluminescence and the Dynamical Casimir Effect	239	(16)
Introduction	239	(3)
The Adiabatic Approximation	242	(2)
Discussion of Form of Force on Surface	244	(3)
Bulk Energy	247	(2)
Dynamical Casimir Effect	249	(6)
Radiative Corrections to the Casimir Effect	255	(10)
Formalism for Computing Radiative Corrections	257	(2)
Radiative Corrections for Parallel Conducting Plates	259	(3)
Other Work	262	(1)
Radiative Corrections for a Spherical Boundary	262	(1)
Conclusions	263	(2)
Conclusions and Outlook	265	(4)
Appendix A Relation of Contour Integral Method to Green's Function Approach	269	(4)
Appendix B Casimir Effect for a Closed String	273	(4)
B.1 Open Strings	275	(2)
Bibliography	277	(16)
Index	293