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Approximation of Dirac Operators with Confining Electrostatic and Lorentz Scalar δ -Shell Potentials.
1Institut für Angewandte Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.
Complex Analysis and Operator Theory
|July 28, 2025
Summary
This study approximates Dirac operators using delta-shell potentials. The research focuses on confining electrostatic and Lorentz scalar potentials, which are impermeable to modeled particles.
Area of Science:
- Mathematical Physics
- Quantum Mechanics
Background:
- Dirac operators are fundamental in relativistic quantum mechanics.
- Approximation methods are crucial for solving complex quantum systems.
- Delta-shell potentials offer a simplified model for localized interactions.
Purpose of the Study:
- To investigate the norm resolvent approximation of Dirac operators with delta-shell potentials.
- To analyze confining electrostatic and Lorentz scalar delta-shell potentials.
- To model particle behavior with impermeable potential supports.
Main Methods:
- Utilizing the norm resolvent sense for approximation.
- Applying mathematical analysis to Dirac operators.
- Investigating the properties of confining potentials.
Main Results:
- Established approximation results for Dirac operators with delta-shell potentials.
- Characterized the behavior of confining electrostatic and Lorentz scalar potentials.
- Demonstrated the impermeability of the potential support to modeled particles.
Conclusions:
- The study provides a rigorous framework for approximating Dirac operators with specific delta-shell potentials.
- The findings contribute to the understanding of quantum particle behavior in confined systems.
- This work extends previous investigations in the field of mathematical physics.
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