Introduction | p. 1 |
Background and Motivation | p. 1 |
Invitation: A Sample Calculation | p. 3 |
Zero-Point Energies: Summing $$ | p. 3 |
From Discrete to Continuous: Phase Shifts and the Density of States | p. 5 |
Counting States: Levinson's Theorem | p. 6 |
Divergences: The Born Approximation | p. 7 |
Computational Techniques | p. 11 |
References | p. 12 |
Review of Scattering Theory | p. 15 |
Scattering Theory in Arbitrary Dimension | p. 15 |
Green's Functions from Scattering Data | p. 18 |
Phase Shifts and Density of States | p. 20 |
Levinson's Theorem and Finite Energy Sum Rules | p. 23 |
Overview and Simplified Derivation | p. 24 |
Proof of the Regular Sum Rules | p. 25 |
The Symmetric Channel in One Dimension | p. 29 |
References | p. 32 |
Quantum Field Theory and the Spectral Method | p. 33 |
Small-Amplitude Quantum Corrections | p. 33 |
The Canonical Formalism | p. 34 |
The Vacuum Energy Density | p. 35 |
The Vacuum Energy | p. 40 |
The Path Integral Approach | p. 41 |
Connecting the Functional and Canonical Formalisms | p. 43 |
Feynman Diagrams and the Born Series | p. 44 |
Some Remarks on Renormalization | p. 52 |
Quantum Energy of Interfaces | p. 55 |
The Interface Formula | p. 56 |
References | p. 60 |
Applications in One Space Dimension | p. 63 |
Vacuum Polarization Energy in Exactly Solvable Models | p. 63 |
Fermions in One Spatial Dimension | p. 67 |
Parity-Invariant Background Fields | p. 67 |
Fermions in the sine-Gordon Background | p. 70 |
Fermions in the Kink Background | p. 72 |
Bosons, Fermions, Supersymmetry, Central Charge, and the BPS Bound | p. 76 |
Fermions | p. 76 |
Supersymmetry and Central Charge | p. 77 |
SVV Anomaly | p. 81 |
Soliton Stabilization by Fermions in d = 1+1 | p. 82 |
The One-Loop Effective Energy | p. 85 |
The Fermion Number | p. 86 |
Results | p. 86 |
References | p. 88 |
Spectral Analysis of Charges | p. 91 |
Basic Idea and Derivation | p. 91 |
Electrostatics and the Need for Regularization | p. 93 |
Chiral Bag Model in One Space Dimension | p. 96 |
Chiral Bag Model in Three Space Dimensions | p. 97 |
References | p. 101 |
Hedgehog Configurations in d = 3+1 | p. 103 |
Chiral Fermions | p. 103 |
The Model | p. 103 |
The Fermion Loop | p. 104 |
Numerical Analysis | p. 110 |
SUL(2) Gauge Theory | p. 116 |
Classical Sphalerons | p. 117 |
Energetically Stabilized Solitons | p. 119 |
The Search for the Soliton | p. 120 |
Beyond the Spherical Ansatz | p. 127 |
References | p. 127 |
Boundary Conditions and Casimir Forces | p. 129 |
Dirichlet Conditions from Quantum Field Theory | p. 131 |
Rigid Bodies: Dirichlet Points and Parallel Plates | p. 132 |
The Casimir Stress on a Dirichlet Ring | p. 136 |
Oversubtraction and Diagrammatic Analysis | p. 139 |
The Dirichlet Sphere | p. 140 |
References | p. 142 |
String-Type Configurations | p. 143 |
Flux Tubes in Quantum Electrodynamics | p. 143 |
The Vortex Configuration | p. 144 |
The Quantum Energy of the Vortex | p. 144 |
Subtleties of Configurations with Net Flux and Embedding | p. 146 |
Numerical Results for the Quantum Energy | p. 148 |
Quantum Energy Density | p. 151 |
Flux Tubes and Strings in the Electroweak Standard Model | p. 153 |
The Bosonic Sector | p. 154 |
The String Solutions | p. 155 |
The Sphaleron Square | p. 155 |
The Fermion Action | p. 157 |
Fermions on Strings | p. 158 |
The Vacuum Polarization Energy | p. 159 |
Numerical Results | p. 163 |
References | p. 168 |
Quantum Corrections to Q-Balls | p. 171 |
The Q-Ball | p. 171 |
Quantum Corrections | p. 173 |
Applications | p. 176 |
References | p. 177 |
Index | p. 179 |
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