Role of Ambiguities and Gauge Invariance in the Calculation of the Radiatively Induced Chern-Simons Shift in Extended Q.E.D.

Abstract

We investigate the possibility of Lorentz and CPT violations in the photon sector, of the Chern-Simons form, be induced by radiative corrections arising from the Lorentz and CPT non-invariant fermionic sector of an extended version of QED. By analyzing the modified vacuum polarization tensor, three contributions are considered: two of them can be identified with well known amplitudes; the (identical) QED vacuum polarization tensor and the (closely related) $AVV$ triangular amplitude. These amplitudes are evaluated in their most general form (to include in our discussion automatically the question of ambiguities) on the point of view of a strategy to manipulate and calculate divergent amplitudes that can avoid the explicit calculation of divergent integrals. Rather than this only general properties are used in intermediary steps. With this treatment, the results obtained by others authors can be easily recovered and we show that, if we choose to impose U(1) gauge invariance maintenance in the pure QED calculated amplitudes, to be consistent with the renormalizability, the induced Chern-Simons term assumes a nonvanishing ambiguities free value. However if, in addition, we choose to get an answer consistent with renormalizability by anomaly cancellation of the Standard Model a vanishing value can be obtained, in accordance with what was previously conjectured by other authors.

15 pages, LaTeX

Cited by in corpus (38)

• Black holes with a cosmological constant in bumblebee gravity
• Lorentz and CPT violations from Chern-Simons modifications of QED
• Magnetic Moment Generation from non-minimal couplings in a scenario with Lorentz-Symmetry Violation
• Aspects of Causality and Unitarity and Comments on Vortex-like Configurations in an Abelian Model with a Lorentz-Breaking Term
• QED with minimal and nonminimal couplings: on the quantum generation of Lorentz violating terms in the pure photon sector
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Feynman propagator for the nonbirefringent CPT-even electrodynamics of the Standard Model Extension
• Gauge propagator and physical consistency of the CPT-even part of the Standard Model Extension
• Radiative generation of the CPT-even gauge term of the SME from a dimension-five nonminimal coupling term
• Influence of Lorentz- and CPT-violating terms on the Dirac equation
• Finite Temperature behavior of the CPT-even and parity-even electrodynamics of the Standard Model Extension
• Aspects of Quantum Corrections in a Lorentz-violating Extension of the Abelian Higgs Model
• Cutoff-independent regularization of four-fermion interactions for color superconductivity
• The photino sector and a confining potential in a supersymetric Lorentz-symmetry-violating model
• Maxwell electrodynamics modified by CPT-even and Lorentz-violating dimension-6 higher-derivative terms
• A Lorentz-violating SO(3) model: discussing the unitarity, causality and the 't Hooft-Polyakov monopoles
• Effects of CPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter
• Dimensional reduction of the CPT-even electromagnetic sector of the Standard Model Extension
• Extension of the Nambu--Jona-Lasinio model at high densities and temperatures by using an implicit regularization scheme
• Classical solutions for the Carroll-Field-Jackiw-Proca electrodynamics
• Stationary solutions for the parity-even sector of the CPT-even and Lorentz-covariance-violating term of the standard model extension
• Maxwell electrodynamics modified by a CPT-odd dimension-five higher-derivative term
• Unitarity in Maxwell-Carroll-Field-Jackiw electrodynamics
• Consistency in Perturbative Calculations and Radiatively Induced Lorentz and CPT Violations
• Parity-odd and CPT-even electrodynamics of the SME at Finite Temperature
• Effective electromagnetic actions for Lorentz violating theories exhibiting the axial anomaly
• Partitioning Dense Graphs with Hardware Accelerators
• Non-relativistic electron-electron interaction in a Maxwell-Chern-Simons-Proca model endowed with a timelike Lorentz-violating background
• A predictive formulation of the Nambu--Jona-Lasinio model
• Anomalies Dismissed of Ambiguities and the Neutral Pion Decay
• Gauge anomalies in Lorentz-violating QED
• Super-entropy bumblebee AdS black holes
• Influence of Lorentz-violating terms on a two-level system
• Renormalization Scheme Dependence of $\beta$-Functions In Lorentz-Violating Quantum Field Theory
• Residual gauge-invariance in a massive Lorentz-violating extension of QED
• On one-loop corrections in the non-minimal dimension-five extension of QED
• Effective electromagnetic Lagrangians in the derivative expansion method
• Optical and Thermodynamic Signatures of Lorentz Symmetry Breaking in Bumblebee AdS Black Holes