Charting the Uncharted: Hamiltonian Truncation and Real-Time Dynamics in Strongly Coupled Field Theories

by Dr Brian Henning (Kavli Institute for Theoretical Physics/UCSB)

Thursday Mar 6, 2025, 3:30 PM → 4:30 PM Pacific/Honolulu

Room 112 (Watanabe Hall)

Strong-coupling phenomena—ranging from exotic meson structures to the rich QCD phase diagram impacting heavy ion collisions, neutron stars, and early-universe transitions—pose challenges that have long eluded our conventional perturbative and lattice tools. In this colloquium, I will present a novel nonperturbative approach based on Hamiltonian truncation (HT), a method that effectively applies the principles of quantum mechanics to field theories by strategically truncating the Hilbert space. My collaborators and I have recently developed the first general recipe to compute scattering amplitudes nonperturbatively from spectral data obtained via HT, thereby accessing the S-matrix—the most fundamental observable in high-energy physics.

I will begin by highlighting the universal need for nonperturbative methods in capturing real-time dynamics, especially where lattice Monte Carlo techniques encounter insurmountable limitations, such as the sign problem and the Euclidean nature of the formulation. I will then review the remarkable successes of HT in 1+1 dimensions, outline promising results in 2+1 dimensions, and discuss ongoing efforts to incorporate dynamical gauge bosons—pushing toward applications in gauge theories like QED3. This theory, a strongly coupled and confining gauge model with deep connections to QCD and condensed matter systems (e.g., high-Tc superconductivity and the fractional quantum Hall effect), serves as a crucial testing ground for our method.

Join me as we explore these new frontiers in Hilbert space, unveiling a fresh, real-time perspective on nonperturbative quantum field theory that could ultimately reshape our understanding of the strong force and beyond.