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math-ph2024★ 3 cited
Propagators in curved spacetimes from operator theory
Jan Dereziński, Christian Gaß
We discuss two distinct operator-theoretic settings useful for describing (or defining) propagators associated with a scalar Klein-Gordon field on a Lorentzian manifold . Typica…
math-ph2024
Point potentials on Euclidean space, hyperbolic space and sphere in any dimension
Jan Dereziński, Christian Gaß, Błażej Ruba
In dimensions d= 1, 2, 3 the Laplacian can be perturbed by a point potential. In higher dimensions the Laplacian with a point potential cannot be defined as a self-adjoint operator…
math-ph2023
Generalized integrals and point interactions
Jan Dereziński, Christian Gaß, Błażej Ruba
First we recall a method of computing scalar products of eigenfunctions of a Sturm-Liouville operator. This method is then applied to Macdonald and Gegenbauer functions, which are…