Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach

Understand

We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods.

• The latter are based on Hamiltonian lattice gauge theory and multi-scale analysis via inductive limits of $C^{*}$-algebras which are applicable in arbitrary dimensions.
• The major step, restricted to one spatial dimension, is the explicitly construction of the spatially-localized von Neumann algebras of time-zero fields in the time gauge in representations associated with scaling limits of Gibbs states of the Kogut-Susskind Hamiltonian.
• We relate our work to existing results about YM$_{1+1}$ and its counterpart in Euclidean quantum field theory (YM$_{2}$).