Paul Romatschke- University of Colorado

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

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, finding that — contrary to widely held and
endlessly repeated beliefs — these systems often do in fact possess a
stable ground state in the quantum world. This realization challenges
statements that have become pillars of high energy physics, such as
the quantum triviality of the Higgs field and reserving asymptotic
freedom only for non-Abelian gauge theories. It’s a revolution in the
making, so please join me for a “sneak-preview” of what’s coming.