Scattering in the pair of Hilbert spaces
Egor Bugrij, Alexei Mishchenko, Yurii Sitenko (Bogolyubov Institute, for Theoretical Physics)
TL;DR
This paper develops a scattering theory framework in a pair of Hilbert spaces to analyze the scattering of a charged particle around a wormhole with magnetic fields, deriving wave operators and S-matrices.
Contribution
It introduces a novel mathematical framework using paired Hilbert spaces for scattering problems involving complex gravitational and magnetic backgrounds.
Findings
Derived modified wave operators for the system
Constructed the S-matrix within the paired Hilbert space framework
Provided a mathematical foundation for scattering in wormhole geometries
Abstract
The problem of the scattering of a charged test particle in the gravitational background of axially symmetrical wormhole in the presence of the Aharonov-Bohm type magnetic field is considered. It is shown that the natural mathematical framework appropriate for the problem is the scattering theory in the pair of Hilbert spaces. Both relevant modified wave operators and -matrices are found.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum Mechanics and Non-Hermitian Physics · Numerical methods in inverse problems