Abstract
In this work we study a z=3 Horava-Lifshitz-like extension of QED in (3+1) dimensions. We calculate the one-loop radiative corrections to the two and three-point functions of the gauge and fermion fields. Such corrections were achieved using the perturbative approach and a dimensional regularization was performed only in the spatial sector. Renormalization was required to eliminate the divergent contributions emergent from the photon and electron self-energies and from the three-point function. We verify that the one-loop vertex functions satisfy the usual Ward identities and using renormalization group methods we show that the model is asymptotically free.
Highlights
The possibility of Lorentz symmetry breaking, which began to be discussed in the early 1990s [1], motivated interest in the idea of space-time anisotropy based on the suggestion that spatial and temporal coordinates enter field theories in distinct ways; the resulting theory involves different orders in the derivatives with respect to time and space coordinates
In this work we study the possibility of symmetry restoration in a z 1⁄4 3 Lifshitz extension of QED in (3 þ 1) dimensions, through the calculation of the oneloop radiative corrections
After obtaining the low momenta contributions to the three point vector-spinor vertex function, we verified that our results satisfy Ward identities which confirm their validity
Summary
The possibility of Lorentz symmetry breaking, which began to be discussed in the early 1990s [1], motivated interest in the idea of space-time anisotropy based on the suggestion that spatial and temporal coordinates enter field theories in distinct ways; the resulting theory involves different orders in the derivatives with respect to time and space coordinates. Some important results were obtained for it in the case z 1⁄4 2, such as the one-loop corrections to the two-point function of the gauge field There it was verified, that the dynamical restoration of the Lorentz symmetry occurs at low energies, at least in certain cases [6]. Throughout this work, we use the Minkowski metric gμν 1⁄4 diagð1; −1; −1; −1Þ
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