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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,341 papers · 148 categories

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6 results for “prequantisation”

The 2-Hilbert Space of a Prequantum Bundle Gerbemath-ph

Constructs 2-Hilbert space for line bundle gerbes.

problem Higher prequantisation and line bundle gerbes.

method Constructs a 2-Hilbert space category from morphism categories of line bundle gerbes.

result Shows the constructed 2-Hilbert space is semisimple and abelian.

2-Hilbert space line bundle gerbe higher prequantisation monoidal structure Waldorf's 2-category

2016-08-30abs ↗pdf ↗

(Re)constructing Lie groupoids from their bisections and applications to prequantisationmath.DG

This paper reconstructs Lie groupoids from their bisections and applies it to prequantisation.

problem Reconstructing Lie groupoids from their bisections and applying it to prequantisation.

method Investigates the relation of bisections to Lie groupoids and constructs Lie groupoids from bisection Lie groups using recent progress in the infinite-dimensional Frobenius theorem.

result Characterizes an integrability constraint of closed Lie subalgebras to closed Lie subgroups in terms of modified discreteness conditions on periods.

Lie groupoids bisections prequantisation infinite-dimensional Frobenius theorem discreteness conditions

2015-06-17abs ↗pdf ↗

On the prequantisation map for 2-plectic manifoldsmath.DG

Abstract: Generalizes prequantization map for 2-plectic manifolds.

problem Generalizing prequantization map for 2-plectic manifolds.

method Constructs a

PU(H)

-bundle and Lie groupoid over the total space of a manifold with an integral closed 3-form.

result Provides a Lie 2-algebra quasi-isomorphism from observables to weak symmetries.

2-plectic manifolds prequantization map Lie groupoid curving gerbes

2020-08-12abs ↗pdf ↗

Gerbes in Geometry, Field Theory, and Quantisationmath.DG

Survey of bundle gerbes in geometry, field theory, and quantization.

problem Exploring bundle gerbes and their applications in geometry, field theory, and quantization.

method Definition and classification of bundle gerbes with connection, surface holonomy, transgression line bundles, and geometric quantization.

result Bundle gerbes provide a smooth bordism-type field theory and geometric quantization for 2-plectic and symplectic forms.

bundle gerbes geometry field theory quantization holonomy

2021-02-20abs ↗pdf ↗

Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisationmath-ph

Develops 2-Hilbert spaces for bundle gerbes in geometric quantization.

problem Higher geometric quantization of bundle gerbes.

method Introduces 2-Hilbert spaces, rig-categories, and duals for bundle gerbes.

result Constructs a 2-Hilbert space of sections for bundle gerbes.

bundle gerbes higher geometric quantization 2-Hilbert spaces rig-categories dimensional reduction

2017-09-18abs ↗pdf ↗

Gaugings of Groupoids, Strings in Shadows, and Emergent Poisson

σ

-Modelshep-th

A new gauge principle for string models emerges from groupoid symmetries.

problem Describing gauge symmetries in 2D non-linear sigma models.

method Introducing principaloid bundles and using twisted equivariant structures.

result Emergence of Poisson sigma models from gauge principles.

gauge principle sigma models groupoids equivariant structures non-linear sigma models

2026-03-21abs ↗pdf ↗