HilbNets discretize Hilbert bundle convolutions through Hilbert Cellular Sheaves whose Laplacians converge to the continuous connection Laplacian, enabling consistent learning across samplings.
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A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
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Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
HilbNets discretize Hilbert bundle convolutions through Hilbert Cellular Sheaves whose Laplacians converge to the continuous connection Laplacian, enabling consistent learning across samplings.
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On the Quantisation of Linear Gauge Theories on Lorentzian Manifolds: Maxwell's Theory via Complete Gauge Fixing
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.