Wilson loops in the Hamiltonian formalism

Abstract

In a gauge theory, the gauge invariant Hilbert space is unchanged by the coupling to arbitrary local operators. In the presence of Wilson loops, though, the physical Hilbert space must be enlarged by adding test electric charges along the loop. I discuss how at nonzero temperature Polyakov loops are naturally related to the propagator of a test charge. 't Hooft loops represent the propagation of a test magnetic charge, and so do not alter the physical Hilbert space.

References in corpus (15)

• Generalized Global Symmetries
• Matrix Product States for dynamical simulation of infinite chains
• Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme
• Effective Theory of Wilson Lines and Deconfinement
• Production and Elliptic Flow of Dileptons and Photons in the semi-Quark Gluon Plasma
• How Wide is the Transition to Deconfinement?
• Suppression of the Shear Viscosity in a "semi" Quark Gluon Plasma
• Second order cumulants of conserved charge fluctuations revisited I. Vanishing chemical potentials
• Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term
• Exact Symmetries and Threshold States in Two-Dimensional Models for QCD
• The 't Hooft loop in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
• Zero Point Energy of Renormalized Wilson Loops
• Gibbs entropy from entanglement in electric quenches
• Matrix Models for Deconfinement and Their Perturbative Corrections
• Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks