Physics / research
Saddles, solitons, and strong-coupling clues
Explore field configurations and controlled expansions beyond ordinary perturbation theory, separating rigorous statements from model-dependent semiclassical evidence.
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Module 01 research
Saddles, solitons, and strong-coupling clues
Explore field configurations and controlled expansions beyond ordinary perturbation theory, separating rigorous statements from model-dependent semiclassical evidence.
- 01
Scalar kinks and topological charge
Construct a finite-energy scalar kink from its boundary values and distinguish topological sectors, local stability, and dynamical scattering.
28 min - 02
Bogomolny bounds and first-order equations
Complete an energy functional into a nonnegative square and boundary term, then distinguish a bound from existence and saturation.
28 min - 03
Vortex solutions in gauge–Higgs models
Connect finite-energy Higgs winding to quantized magnetic flux and derive a critically coupled vortex tension bound with explicit normalization.
29 min - 04
’t Hooft–Polyakov monopoles
Relate the adjoint Higgs boundary map to a smooth magnetic monopole and derive its BPS mass with a canonical gauge-coupling convention.
29 min - 05
Euclidean instanton actions and collective coordinates
Derive the Yang–Mills instanton bound with explicit trace conventions and identify the measure and boundary assumptions behind a semiclassical sector.
30 min - 06
Tunneling determinants and zero modes
Separate Gaussian fluctuation factors from collective-coordinate measures, with explicit boundary conditions and a distinction between level splitting and decay.
30 min - 07
False-vacuum decay and bounce solutions
Derive the thin-wall Euclidean bounce exponent and distinguish its negative mode, collective translations, and decay-rate interpretation.
30 min - 08
Large-N vector-model saddles
Turn an O(N) invariant integral into a collective-variable saddle and connect its controlled finite-dimensional example to regulated field-theory gap equations.
30 min - 09
Resurgence in quantum-mechanical examples
Fix a Borel convention, analyze controlled factorial-series examples, and explain how global spectral conditions enter quantum-mechanical transseries.
31 min - 10
Confinement criteria and semiclassical regimes
State a Wilson-loop confinement criterion and examine a controlled compactified gauge regime without extrapolating its semiclassical expansion beyond its hierarchy.
31 min