Continuum Limits for Discrete Dirac Operators on 2D Square Lattices
Offered By: Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube
Course Description
Overview
Explore a mathematical lecture on the continuum limits of discrete Dirac operators on 2D square lattices. Delve into the proposed embedding of $\ell^2(\mathbb Z_h^d)$ into $L^2(\mathbb R^d)$, enabling the comparison of discrete and continuum Dirac operators in $L^2(\mathbb R^2)^2$. Examine the proof of strong resolvent convergence for discrete Dirac operators to continuum Dirac operators, considering bounded and uniformly continuous potentials on $\mathbb R^2$. Investigate the lack of norm resolvent convergence and its connection to the absence of the Liouville theorem in discrete complex analysis. This 41-minute talk, presented by Tomio Umeda at the Erwin Schrödinger International Institute for Mathematics and Physics, was part of the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" in November 2022.
Syllabus
Tomio Umeda - Continuum limits for discrete Dirac operators on 2D square lattices
Taught by
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)
Related Courses
Maria Esteban - Spectral Results and Open Problems for Dirac-Coulomb Operators With Charge DistributionsInstitute for Pure & Applied Mathematics (IPAM) via YouTube Curvature of the Determinant Line Bundle for Noncommutative Tori
Hausdorff Center for Mathematics via YouTube A Fixed-Point Formula for Dirac Operators on Lie Groupoids
Fields Institute via YouTube Homological Methods in Random Noncommutative Geometry
Fields Institute via YouTube Families of Dirac Operators and Applications
ICTP Mathematics via YouTube