Life on an Endless Hill: Making Sense of Up-Side-Down Potentials in Quantum Mechanics and High Energy Physics

Abstract: In classical physics, unbounded (or "up-side-down")
potentials do not allow for a stable ground state. As a consequence,
unbounded potentials have often been dismissed as not viable for
proper unitary quantum theories. Historically, we have learned that
the quantum world often contradicts dearly held beliefs based on
classical physics. By contrast, mathematics has been recognized as a
good guide even when classical intuition fails.  In this talk, I will
use well-developed mathematics to explore physical systems with
up-side-down and non-Hermitian potentials in quantum mechanics and
quantum field theory, with applications to AMO experiments, high
energy physics and Quantum Chromodynamics.