Speaker
Description
Hamiltonian lattice gauge theory, free from the sign problem, is regarded as a promising framework for real-time dynamics and finite-density physics. In this talk I propose an analytical approach to it, based on techniques from topological quantum field theory (TQFT). The gauge-invariant Hilbert space is constructed naturally, with charges and fluxes organized by the quantum double $D(G)$, and matrix elements can be evaluated by topological methods. The electric and magnetic descriptions are then related by electromagnetic duality, which keeps the formulation well suited to the continuum limit. I will illustrate the approach with several concrete examples, including non-abelian finite groups and their quantum-group deformations, with QCD and its magnetic basis as the eventual target.