Confinement and Deconfinement in Gauge Theories - A Quantum Field Theory Perspective

Explore the intricacies of gauge theories in this comprehensive lecture by A. P. Balachandran from Syracuse University. Delve into the concepts of small and large gauge transformations, and gain insights into the nature of observables. Examine the infinite superselection sectors in gauge theories, classified by large gauge transformations, and understand how gauge theory sectors are labeled by eigenvalues of a complete commuting set (CCS) of these transformations. Investigate the standard chemical potential in QED as an operator generating global U(1), and discover additional operators derived from electric field moments on the sphere at infinity. Learn about the construction of CCS in QCD using two commuting generators spanning a Cartan subalgebra. Understand how elements of large gauge transformations can be added to the standard Hamiltonian as chemical potentials without altering field equations, and explore their role in creating confined and deconfined phases in QCD. Conclude with a speculation on the physical significance of these chemical potentials, providing a deeper understanding of confinement and deconfinement in gauge theories within the framework of quantum field theory.