Remarks on discrete Dirac operators and their continuum limits

👤 中村周

🗒

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted particles (spectral subspaces), and this phenomenon is known as the fermion doubling. In order to overcome this difficulty, two methods were proposed.
(1) Introduce a new term, called the Wilson term;
(2) The KS-fermion model or the staggered fermion model.
We discuss mathematical formulations of these, and study their continuum limits. The preprint is available at https://arxiv.org/abs/2306.14180.