Causality and dimensionality in geometric scattering

• URL: http://arxiv.org/abs/2112.02733v2
• Date: Mon, 4 Apr 2022 23:02:19 GMT
• Title: Causality and dimensionality in geometric scattering
• Authors: Silas R. Beane and Roland C. Farrell
• Abstract summary: The scattering matrix describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials. The effect of spatial dimensionality is investigated by considering scattering in two and three dimensions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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