Contributions to Potential Scattering

Doctoral thesis, Universidad de Zaragoza, Department of Theoretical Physics, 1995

The thesis studies scattering on the line through the scattering matrix. It builds the Jost and inverse-scattering machinery in one dimension, finds supersymmetric factorisations already present in the radial measure of rank-one symmetric spaces, follows bound states and resonance poles as a coupling varies, classifies the four-parameter family of contact interactions supported at a point, and lets the scale act directly on the S matrix as a renormalisation group whose fixed points are the scale-invariant contacts.

The two editions

• Contributions to Potential Scattering, revised English edition2026; 110 pages, 1.9 MB
• Contribución al estudio de scattering potencialthe Spanish original, as typeset again in June 2001; 149 pages, 1.2 MB

The English edition was translated and scientifically updated with GPT in 2026. Its equations were recalculated, its conventions made consistent and its bibliography brought up to date. The mark (2026) flags connections with later literature; (2026-gpt) flags calculations and constructions added for this edition. Original equation and section numbers are kept, and the appendices account for every original equation, figure and bibliography entry. The title page links to the Spanish original in this same directory.

Chapters

1. Scattering in one dimension
2. Supersymmetry and scattering on homogeneous spaces
3. Trajectories and poleology
4. Point-supported interactions
5. The renormalisation group