arXiv subjects

Kerr Maxwell

Publications and source records attributed to Kerr Maxwell.

3 recordsLinked to original sources

arXiv2025

Non-Symplectic Deformations of Geometric Quantisation

We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks of prequantum data by non-symplectic diffeomorphisms. Our main result is deriving the equations of motion for some simple pseudo-quantisations. We also compute the pseudo-quantisation of several simple examples from symplectic and almost-symplectic geometry, as well as the general form of the resulting deformed canonical commutator.

math-ph↗

arXiv2025

Structured Gaussians From Geometric Quantisation

We develop a geometric description of structured Gaussian beams, a form a structured light, by applying geometric quantisation and symplectic reduction to the 2D harmonic oscillator. Our results show that the geometric quantisation of the oscillator's reduced phase space coincides with the modal Poincar\'e sphere in optics. We explicitly consider the case of the Generalised Hermite-Laguerre-Gauss modes, identifying their interbasis expansions with rotations of the reduced phase space and the geometric data accompanying the quantisation. This description simplifies the presentation of $SU(2)$ symmetries in structured light beams and is extensible to other symmetry groups.

physics.optics↗

arXiv2024

Stochastic Stokes origami: folds, cusps and skyrmionic facets in random polarisation fields

We consider the jacobian of a random transverse polarisation field, from the transverse plane to the Poincar\'e sphere, as a Skyrme density partially covering the sphere. Connected domains of the plane where the jacobian has the same sign -- patches -- map to facets subtending some general solid angle on the Poincar\'e sphere. As a generic continuous mapping between surfaces, we interpret the polarisation pattern on the sphere in terms of fold lines (corresponding to the crease lines between neighbouring patches) and cusp points (where fold lines meet). We perform a basic statistical analysis of the properties of the patches and facets, including a brief discussion of the percolation properties of the jacobian domains. Connections with abstract origami manifolds are briefly considered. This analysis combines previous studies of structured skyrmionic polarisation patterns with random polarisation patterns, suggesting a particle-like interpretation of random patches as polarisation skyrmionic anyons.

physics.optics↗