Alladi Ramakrishnan Hall

Lectures on Algebraic Quantum Theory

A. P. Balachandran

Syracuse University

Last lecture: Confinement and Deconfinement in Gauge Theories: A Quantum Field Theory

After a brief discussion of small and large gauge transformations
and the nature of observables, we discuss superselection sectors in gauge
theories. There are an infinity of them, classified by large gauge
transformations. Gauge theory sectors are labeled by the eigenvalues of a
complete commuting set (CCS) of these transformations.
In QED, the standard chemical potential is one such operator generating
global U(1). There are many more given by the moments of the electric field
on the sphere at infinity. In QCD, the CCS are constructed from the two
commuting generators spanning a Cartan subalgebra.
We show that any element of a large gauge transformation can be
added to the standard Hamiltonian as a chemical potential without changing
field equations and that in QCD, they lead to confined and deconfined
phases. A speculation about the physical meaning of these chemical
potentials is also made.
Zoom link
zoom.us/j/96427034036
Meeting ID: 964 2703 4036
Passcode: 720968