Electromagnetic current correlations in reduced quantum electrodynamics

S. Teber

doi:10.1103/PhysRevD.86.025005

paper

Electromagnetic current correlations in reduced quantum electrodynamics

arXiv:1204.5664 · doi:10.1103/PhysRevD.86.025005

Abstract

We consider a theory of massless reduced quantum electrodynamics (RQED $_{d_{γ}, d_{e}}$ ), e.g., a quantum field theory where the U(1) gauge field lives in $d_{γ}$ -spacetime dimensions while the fermionic field lives in a reduced spacetime of $d_{e}$ dimensions ( $d_{e} ⩽ d_{γ}$ ). In the case where $d_{γ} = 4$ such RQEDs are renormalizable while they are super-renormalizable for $d_{γ} < 4$ . The 2-loop electromagnetic current correlation function is computed exactly for a general RQED $_{d_{γ}, d_{e}}$ . Focusing on RQED $_{4, 3}$ , the corresponding $β$ -function is shown to vanish which implies the scale invariance of the theory. Interaction correction to the 1-loop vacuum polarization, $Π_{1}$ , of RQED $_{4, 3}$ is found to be: $Π= Π_1 (1 + 0.056 \al)$ where $\al$ is the fine structure constant. The scaling dimension of the fermion field is computed at 1-loop and is shown to be anomalous for RQED $_{4, 3}$ .

(v2) Accepted for publication in PRD. Conclusion and references added (some / referee's comments). No change in results. 8 pages, 3 figures. (v1) LaTeX file with feynMF package. 8 pages, no figure

Electromagnetic current correlations in reduced quantum electrodynamics

Abstract

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