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Register a new userRevealing hidden symmetries and gauge invariance of the massive Carroll-Field-Jackiw model
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In this paper we have analyzed the improved version of the Gauge Unfixing (GU) formalism of the massive Carroll-Field-Jackiw model, which breaks both the Lorentz and gauge invariances, to disclose hidden symmetries to obtain gauge invariance, the key stone of the Standard Model. In this process, as usual, we have converted this second-class system into a first-class one and we have obtained two gauge invariant models. We have verified that the Poisson brackets involving the gauge invariant variables, obtained through the GU formalism, coincide with the Dirac brackets between the original second-class variables of the phase space. Finally, we have obtained two gauge invariant Lagrangians where one of them represents the Stueckelberg form.
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In this work we focus on the Carroll-Field-Jackiw (CFJ) modified electrodynamics in combination with a CPT-even Lorentz-violating contribution. We add a photon mass term to the Lagrange density and study the question whether this contribution can render the theory unitary. The analysis is based on the pole structure of the modified photon propagator as well as the validity of the optical theorem. We find, indeed, that the massive CFJ-type modification is unitary at tree-level. This result provides a further example for how a photon mass can mitigate malign behaviors.
In this paper we analyze a generalized Jackiw-Rebbi (J-R) model in which a massive fermion is coupled to the kink of the $lambdaphi^4$ model as a prescribed background field. We solve this massive J-R model exactly and analytically and obtain the whole spectrum of the fermion, including the bound and continuum states. The mass term of the fermion makes the potential of the decoupled second order Schrodinger-like equations asymmetric in a way that their asymptotic values at two spatial infinities are different. Therefore, we encounter the unusual problem in which two kinds of continuum states are possible for the fermion: reflecting and scattering states. We then show the energies of all the states as a function of the parameters of the kink, i.e. its value at spatial infinity ($theta_0$) and its slope at $x=0$ ($mu$). The graph of the energies as a function of $theta_0$, where the bound state energies and the two kinds of continuum states are depicted, shows peculiar features including an energy gap in the form of a triangle where no bound states exist. That is the zero mode exists only for $theta_0$ larger than a critical value $(theta_0^{textrm{c}})$. This is in sharp contrast to the usual (massless) J-R model where the zero mode and hence the fermion number $pm1/2$ for the ground state is ever present. This also makes the origin of the zero mode very clear: It is formed from the union of the two threshold bound states at $theta_0^{textrm{c}}$, which is zero in the massless J-R model.
We demonstrate explicitly the absence of the quantum corrections to the Carroll-Field-Jackiw (CFJ) term beyond one-loop within the Lorentz-breaking CPT-odd extension of QED. The proof holds within two prescriptions of quantum calculations, with the axial vector in the fermion sector {}treated either as a perturbation or as a contribution in the exact propagator of the fermion field.
The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d=2(N+1) is analyzed.We first exhibit the underlying group-theoretical clash between locality,gauge,Lorentz and conformal invariance require- ments. Improved traceless stress tensors are then constructed;each violates one of the above criteria.However,when d=N+2,there is a duality equivalence between N-form models and massless scalars.Here we show that conformal invariance is not lost,by constructing a quasilocal gauge invariant improved stress tensor.The correlators of the scalar theory are then reproduced,including the latters trace anomaly.
We reassess an alternative CPT-odd electrodynamics obtained from a Palatini-like procedure. Starting from a more general situation, we analyze the physical consistency of the model for different values of the parameter introduced in the mass tensor. We show that there is a residual gaugeinvariance in the model if the local transformation is taken to vary only in the direction of the Lorentz-breaking vector.
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