Audrey Lindsay | Searcharxiv

arXiv2025

Symmetries of de Sitter Particles and Amplitudes

We discuss the symmetry aspects of quantum field theory in global four-dimensional de Sitter spacetime linked to $SO(1,4)$ isometries. For the unitary irreducible representations relevant to elementary particles, we obtain explicit transformation laws for the symmetry generators acting on one-particle states in a basis adapted to the $SU(2) \times SU(2)'$ decomposition of the Hilbert space. Using these results, we derive the corresponding Ward identities and demonstrate how global spacetime symmetries constrain de Sitter scattering amplitudes. We show that the Poincar\'e algebra and flat-space Ward identities are recovered in the large-momentum limit.

hep-th↗

arXiv2025

On the Learnability of Knot Invariants: Representation, Predictability, and Neural Similarity

We analyze different aspects of neural network predictions of knot invariants. First, we investigate the impact of different knot representations on the prediction of invariants and find that braid representations work in general the best. Second, we study which knot invariants are easy to learn, with invariants derived from hyperbolic geometry and knot diagrams being very easy to learn, while invariants derived from topological or homological data are harder. Predicting the Arf invariant could not be learned for any representation. Third, we propose a cosine similarity score based on gradient saliency vectors, and a joint misclassification score to uncover similarities in neural networks trained to predict related topological invariants.

math.GT↗