Generalized two-dimensional Abelian gauge theories and confinement

Theta Vacuum in Different Gauges

“…Before we end this section, we want to show how a 2π periodicity in θ may enter the theory, getting thereby also a clearer understanding of the role of the unitary operator U, (14). Usually, the 2π periodicity of θ is a consequence of the fact that only gauge fields with integer instanton numbers contribute to VEVs of physical observables.…”

“…Observe that nothing so far depended on the boundary conditions of the gauge transformations λ, i.e., whether w The operator U, (14), maps different |θ states into each other,…”

“…In the following we choose Lorentz gauge ∂ µ A µ = 0 (which is covariant), because there the wellknown operator solution [12,13,14] is at hand. In fact, our presentation will closely follow Chapter 10 of [13].…”

BRST cohomology and vacuum structure of two-dimensional chromodynamics

“…[14]. In the case of the Schwinger model [9] and its generalization to the Cartan subalgebra of U(N) [15], the vacuum is infinitely degenerate. In the U(1) case this is known since the work of Lowenstein and Swieca [10]; in the framework of section 4, these vacua are given by |Ψ 0 = |J, −J , and the infinite degeneracy is a consequence of J taking all integer values.…”

On the U(1)-Problem of QED2

“…This ensures the correct assignment of expectation values to operators with nonvanishing chiral charge. A model similar to (10) but without Thirring term was discussed in [7] using an operator approach. Using the bosonized version of the model we were able to prove the following theorem [5] that generalizes the N=1 proof by Fröhlich [6].…”