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Vacuum polarization in $d+{1/2}$ dimensions

C. D. Fosco·A. P. C. Malbouisson·I. Roditi
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Abstract

We study the main properties of the one-loop vacuum polarization function ($Π_{αβ}$) for spinor $QED$ in `$d + {1/2}$ dimensions', i.e., with fields defined on ${\mathcal M} \subset {\mathbb R}^{d+1}$ such that ${\mathcal M} = \{(x_0,...,x_d) | x_{d}\geq 0 \}$, with bag-like boundary conditions on the boundary $\partial{\mathcal M} = \{(x_0,...,x_d) | x_{d}= 0 \}$. We obtain an exact expression for the induced current due to an external constant electric field normal to the boundary. We show that, for the particular case of 2+1 dimensions, there is a transverse component for the induced current, which is localized on a region close to $\partial{\mathcal M}$. This current is a parity breaking effect purely due to the boundary.

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C. D. Fosco, A. P. C. Malbouisson, I. Roditi. 2005-02-02. Vacuum polarization in $d+{1/2}$ dimensions. https://doi.org/10.1016/j.physletb.2005.01.049

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