Higher derivative Chern-Simons extension in the noncommutativeQED3

Abstract

The noncommutative (NC) massive quantum electrodynamics in 2 + 1 dimensions is considered. We show explicitly that the one-loop effective action arising from the integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are obtained. Moreover, the gauge invariance of the outcome action is carefully discussed. We then consider the higher-derivative modification into the pure NC Chern-Simons Lagrangian density and evaluate the one-loop correction to the pole of the photon propagator.

One-loop photon’s effective action in the noncommutative scalar QED3

“…These contributions are the same as in the NC-scalar QED 3 because the additional graph is identically zero. Thus, it is easy to realize that the final result in the parity preserving sector for both cases is the same [24]. The last type of diagrams is for n = 4 legs, that for the fermionic case we have the contribution of the box diagram only, i.e.…”

“…where Tr is a sum over eigenvalues of the operator inside the bracket which can also be evaluated in momentum space. Similarly to the description of one-loop effective action for the gauge field in the case of NC-QED [24], one can show that Γ eff [A] has a convergent series expansion in coupling constant e. From a diagrammatic point of view, it includes the one-loop graphs contributing to the gauge field n-point functions which is considered as…”

“…We can understand this result from the charge conjugation invariance of the scalar QED in any space-time dimension, known as Furry's theorem, that forbids the presence of an odd number of photon lines in the case of commutative theory. Another important aspect from our analysis is the absence of the Chern-Simons self coupling ǫ µνλ A µ ⋆ A ν ⋆ A λ for the noncommutative scalar QED 3 effective action (3.11), which is only generated in the case of fermionic electrodynamics [24]. σ σ σ Figure 3: Relevant graphs for the induced AAAA-term.…”

“…According to this reasoning, we can also discuss the gauge invariance of the higher-derivative terms generated by considering the next to leading order O(m −3 ) of our expansion. Actually, it is possible to make use of a dimensional analysis, based on arguments of gauge invariance, to establish the pertubative generation of all possible gauge invariant higher-derivative terms in the one-loop effective action [24]. As an example, if we consider all of the O(m −3 ) contributions up to the diagrams with n = 6 external photon legs, we can generate the following effective higher-derivative Lagrangian…”

“…NC field theories have been studied through the effective action approach, where the behavior of the new couplings was deeply analyzed [19], where the presence of UV/IR mixing in the 1PI functions signals that applying the usual Wilsonian field theory notions and techniques to NC QFT's one should be careful. This type of analysis was also developed to two and three-dimensional NC models [20][21][22][23][24]. These studies of effective action in 3D models were exclusive to the coupling of gauge and fermion fields, no much attention has been paid to the case involving scalar fields, in particular the case of spinless charged fields interacting with photons.…”