Abstract
Using the Zumino identities it is shown that in a class of non-local gauges, massless QED3 has an infrared behaviour of a conformal field theory with a continuously varying anomalous dimension of the fermion. In the usual Lorentz gauge, the fermion propagator falls off exponentially for a large separation, but this apparent fermion mass is a gauge artifact.
Highlights
Massless QED in 2+1 dimensions has very interesting features
We know the iR behaviour of the Green functions to all orders for a particular choice of the gauge parameter in a specific non-local gauge
It is of interest to know how the Green functions behave in a conventional gauge such as the Lorentz gauge
Summary
Where S is the gauge-invariant Euclidean action. jμ is the source for the vector potential Aμ, and the Grassmann variables η and ηare the sources for the fermions. Integrating this equation, we relate the fermion propagator evaluated with two different gauge functions: Sγδ(x, y) = exp − F − F 0 xy Sγ0δ(x, y). For this particular value of gauge parameter (call it α0) the iR behaviour of the fermion propagator is that of the free theory with no anomalous dimension: Sα0(x, y). Eq (34) suggests that the iR behaviour for other values of α is again a CFT, albeit with a non-zero anomalous dimension for the fermion We may check this by obtaining the dependence of the four-fermion Green function δ4Z Sγ1,γ2;δ1δ2 (x1, x2; y1, y2) = δηγ (x1)δηγ (x2)δηδ (y1)δηδ (y2) j=η=η=0.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
