Electromagnetic current correlations in reduced quantum electrodynamics

Abstract

We consider a theory of massless reduced quantum electrodynamics (RQED${}_{d_{\gamma },d_e}$), e.g., a quantum field theory where the U(1) gauge field lives in $d_{\gamma }$-spacetime dimensions while the fermionic field lives in a reduced spacetime of $d_e$ dimensions ($d_e⩽d_{\gamma }$). In the case where $d_{\gamma }=4$ such RQEDs are renormalizable while they are super-renormalizable for $d_{\gamma }<4$. The 2-loop electromagnetic current correlation function is computed exactly for a general RQED${}_{d_{\gamma },d_e}$. Focusing on RQED${}_{4,3}$, the corresponding $\beta$-function is shown to vanish which implies the scale invariance of the theory. Interaction correction to the 1-loop vacuum polarization, ${\Pi }_1$, 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

References in corpus (3)

• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Minimal conductivity in graphene: interaction corrections and ultraviolet anomaly
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Cited by in corpus (3)

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• Interaction corrections to the minimal conductivity of graphene via dimensional regularization
• Note on an application of the method of uniqueness to reduced quantum electrodynamics