Abstract
We investigate the vacuum state of a charged scalar field [Formula: see text] coupled to two different electromagnetic (EM) backgrounds on two different spaces. (i) [Formula: see text] is first defined on cylindrical space E2 × S1 with compact direction z ∈ S1 having circumference L3. This spatial compactification enables (but does not compel) an EM vacuum density j3 to flow around the spatial cylinder, parallel to z. However, a nonzero gauge potential A3 prefers one direction around z over the other, causing j3 to become nonzero. We analyze this situation for A3 = A3 (y) an arbitrary function of coordinate y, with A0,1,2 = 0. (ii) [Formula: see text] is next defined on Minkowski spacetime in the presence of a background EM plane wave of arbitrary shape and amplitude. As the plane wave sweeps through the charged virtual particle sea at the speed of light it locally excites or churns the sea, making the vacuum nonstationary (without producing vacuum pairs). This nonstationary excitation of the vacuum is nondissipative. A summary of recent calculations is presented. These two examples clearly display that, in gauge theory, potentials are more fundamental then fields.
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