Non-perturbative quantization of Lagrangian quantum field theories for strongly coupled topological systems

Develop non-perturbative quantization methods for Lagrangian quantum field theories that apply to strongly coupled topological quantum systems, providing a consistent treatment of global topological degrees of freedom and flux quantization beyond perturbation theory.

Background

The paper argues that Lagrangian descriptions of gauge theories, such as abelian Chern–Simons models used for fractional quantum Hall (FQH) systems, typically capture only local gauge potentials and miss the global topological data crucial for topological phases. This leads to conflicts with flux quantization when effective fractional charges are modeled.

The authors emphasize that addressing these issues requires a non-perturbative framework, since perturbative quantization cannot encode the necessary global structure. They point out that this gap is part of a long-standing challenge in mathematical physics, akin to the general mass gap problem.

Their work proposes a non-Lagrangian, homotopy-theoretic approach based on classifying spaces and exotic (non-abelian) cohomology, but the broader open challenge of developing general non-perturbative quantization methods for Lagrangian theories remains.