Compactification at finite temperature in noncompact electrodynamics

Abstract

Through the compactification of Euclidean time at finite temperature T, the time component A 0 of the gauge potential in noncompact electrodynamics becomes an angular variable: − π ≤ T −1 A 0 ≤ π. A 0 is locally compact, not in the context of the temperature gauge theory, but as a scalar variable in an effective scalar theory S eff[ A 0] defined by integration over all fields except A 0. In this new context the angular nature of A 0 represents the effects of thermal interactions in the temperature gauge theory. An approximation to S eff[ A 0] is calculated under the two assumptions A 0 ≈ constant, A 1 = 0. The resulting effective actions for scalar and spinor electrodynamics in s + 1 Euclidean dimensions are compact generalizations of the static sine-Gordon theory in s spatial dimensions. As the approximate and exact actions are both compact, we expect our generalized sine-Gordon action to provide a good interpolating description over a wide range of temperature and coupling strength. Noncompact electrodynamics QED s + 1 is shown to screen (confine) integral (nonintegral) charge at finite T, with confinement vanishing smoothly in the limits T → ∞ for s ≥ 1, and T → 0 for s ≥ 2. Thus noncompact QED s + 1 at finite T behaves much like the massive Schwinger model, with the thermal interaction being responsible for electric flux tube formation. A careful study of this parallel with the Schwinger model is presented.