Causality and dimensionality in geometric scattering
arXiv:2112.02733 · doi:10.1016/j.aop.2022.168841
Abstract
The scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly arXiv:2011.01278. In the case of zero-range forces, causality leads to constraints on scattering trajectories in the geometric picture. The effect of spatial dimensionality is also investigated by considering scattering in two and three dimensions. In the geometric formulation it is found that dimensionality is encoded in the phase of the harmonic potential that appears in the geometric action.
18 pages, 4 figures. References and clarifications added in v2
References in corpus (4)
- Ground state energy of the interacting Bose gas in two dimensions: an explicit construction
- Radio frequency spectra of Feshbach molecules in quasi-two dimensional geometries
- Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap
- Classical geodesics from the canonical quantisation of spacetime coordinates