| 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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