Higher derivative Chern-Simons extension in the noncommutative QED3_{3}

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.Comment: 20 pages, published versio

Perturbative quantization of two-dimensional space-time noncommutative QED

Using the method of perturbative quantization in the first order approximation, we quantize a non-local QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e^2,\theta^3), where e is the NC-QED coupling constant and \theta is the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified field variables that satisfy the ordinary equal-time commutation relations up to O(e^2,\theta^3. Using these commutation relations, the canonical current algebra of the modified theory is also derived.Comment: 22 pages, no figure

Impossibility of obtaining a CP-violating Euler-Heisenberg effective theory from a viable modification of QED

In this paper, we examine the CP-violating term of the Euler-Heisenberg action. We focus in the aspects related with the generation of such a term from a QED-like model in terms of the effective action approach. In particular, we show that the generation of the CP-violating term is closely related with both of vector and axial fermionic bilinears. Although, these anomalous models are not a "viable" extension of QED, we argue that the CP-violating term in the photon sector is obtained only from this class of models, and not from any fundamental field theory.Comment: 6 page

Induced Maxwell-Chern-Simons Effective Action in Very Special Relativity

In this paper, we study the one-loop induced photon's effective action in the very special relativity electrodynamics in $(2+1)$ spacetime (VSR-QED$_{3}$). Due to the presence of new nonlocal couplings resulting from the VSR gauge symmetry, we have additional graphs contributing to the $\langle AA\rangle$ and $\langle AAA \rangle$ amplitudes. From these contributions, we discuss the VSR generalization of the Abelian Maxwell-Chern-Simons Lagrangian, consisting in the dynamical part and the Chern-Simons-like self-couplings, respectively. We use the VSR-Chern-Simons electrodynamics to discuss some non-Ohmic behavior on topological materials, in particular VSR effects on Hall's conductivity. In the dynamical part of the effective action, we observe the presence of a UV/IR mixing, due to the entanglement of the VSR nonlocal effects to the quantum higher-derivative terms. Furthermore, in the self-coupling aspect, we verify the validity of the Furry's theorem in the VSR-QED$_{3}$ explicitly.Comment: 19 pages, 3 figure