The massless Dirac equation in two dimensions: zero-energy obstructions and dispersive estimates

• Published in: Journal of spectral theory Vol. 11; no. 3; pp. 935 - 979
• Main Authors: Erdoğan, M. Burak, Goldberg, Michael, Green, William R.
• Format: Journal Article
• Language: English
• Published: European Mathematical Society Publishing House 01.01.2021
• Subjects: Dirac equation; Eigenvalues; Mathematical research; Resonance; United States
• ISSN: 1664-039X; 1664-0403
• DOI: 10.4171/jst/362

We investigate L^1\to L^\infty dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural t^{-\frac{1}{2}} decay rate, which may be improved to t^{-\frac{1}{2} - \gamma} for any 0\leq \gamma<\frac{3}...