Quantum scattering on a delta potential in ghost-free theory

Understand

We discuss the quantum-mechanical scattering of a massless scalar field on a $\delta$-potential in a ghost-free theory and obtain analytic solutions for the scattering coefficients.

• Due to the non-locality of the ghost-free theory the transmission coefficient tends to unity for frequencies much larger than the inverse scale of non-locality, even for infinitely strong potentials.
• At the same time there exists a critical strength of the $\delta$-potential barrier below which there is always a frequency that is totally reflected.
• These scattering properties in ghost-free theories are quite generic and distinguish them from local field theories.