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.
arXiv comment18 pages, 4 figures. References and clarifications added in v2
References in corpus (22)
- Universality in Few-body Systems with Large Scattering Length
- Nuclear effective field theory: status and perspectives
- Interatomic collisions in a tightly confined Bose gas
- Confinement induced molecules in a 1D Fermi gas
- Lecture Notes on General Relativity
- Entanglement Suppression and Emergent Symmetries of Strong Interactions
- How short is too short? Constraining zero-range interactions in nucleon-nucleon scattering
- Celestial Amplitudes from UV to IR
- Quantum Bose-Bose droplets at a dimensional crossover
- Causality and the effective range expansion
- Low Energy Theorems For Nucleon-Nucleon Scattering
- Five lectures on effective field theory
- Causality and universality in low-energy quantum scattering
- Geometry and entanglement in the scattering matrix
- Dimensional crossover of nonrelativistic bosons
- 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
- Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances
- Removing the Wigner bound in non-perturbative effective field theory
- Dimensional crossover in non-relativistic effective field theory
- Classical geodesics from the canonical quantisation of spacetime coordinates