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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Defines a Dirichlet-to-Neumann map for the spectral fractional Laplacian with inhomogeneous data, analyzes the inverse problem of recovering information from it, and proves a density result.
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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.
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Inverse problems for the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data
Defines a Dirichlet-to-Neumann map for the spectral fractional Laplacian with inhomogeneous data, analyzes the inverse problem of recovering information from it, and proves a density result.