Effective Energy for QED₂₊₁ with Semi-Localized Static Magnetic Fields: A Solvable Model
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We evaluate the exact ${\rm QED}_{2+1}$ effective energy for charged spin zero and spin half fields in the presence of a family of static magnetic field profiles localized in a strip of width $\lambda$. The exact result yields an infinite set of relations between the terms in the derivative expansion of the effective energy for a general magnetic field. Upon addition of the standard Maxwell magneto-static energy, the minimum energy configuration at fixed flux corresponds to a uniform magnetic field.
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