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Register a new userNo radiative generation of Chern-Simons-like term in Lorentz-violating QED: dealing with IR divergences
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The issue intensively claimed in the literature on the generation of a CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction -- the axial coupling of fermions with a constant vector field $b_m$ -- is mistaken. The presence of massless gauge field triggers IR divergences that might show up from the UV subtractions, therefore, so as to deal with the (actual physical) IR divergences, the Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL renormalization method, has to be adopted. The proof on the non generation of such a Chern-Simons-like term is done, independent of any kind of regularization scheme, at all orders in perturbation theory.
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We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable.
The radiative induction of the CPT and Lorentz violating Chern-Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector $b_mu$ when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by the quantum corrections. As a complement we obtain that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.
We demonstrate generation of the two-dimensional Chern-Simons-like Lorentz-breaking action via an appropriate Lorentz-breaking coupling of scalar and spinor fields at zero as well as at the finite temperature and via the noncommutative fields method and study the dispersion relations corresponding to this action.
Introducing a chemical potential in the functional method, we construct the effective action of QED$_3$ with a Chern-Simons term. We examine a possibility that charge condensation $langlepsi^daggerpsi rangle$ remains nonzero at the limit of the zero chemical potential. If it happens, spontaneous magnetization occurs due to the Gauss law constraint which connects the charge condensation to the background magnetic field. It is found that the stable vacuum with nonzero charge condensation is realized only when fermion masses are sent to zero, keeping it lower than the chemical potential. This result suggests that the spontaneous magnetization is closely related to the fermion mass.
We study dynamical symmetry breaking in three-dimensional QED with a Chern-Simons (CS) term, considering the screening effect of $N$ flavor fermions. We find a new phase of the vacuum, in which both the fermion mass and a magnetic field are dynamically generated, when the coefficient of the CS term $kappa$ equals $N e^2/4 pi$. The resultant vacuum becomes the finite-density state half-filled by fermions. For $kappa=N e^2/2 pi$, we find the fermion remains massless and only the magnetic field is induced. For $kappa=0$, spontaneous magnetization does not occur and should be regarded as an external field.
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