| So far, the study of Lorentz violation has been lasting for more than20years.Although no departure from Lorentz invariance has yet been detected experimentally,there is no reason to believe that Lorentz invariance would be intact at all energies. Asa matter of fact, there are reasons to suspect its exactness in the context of stringtheory. For example, the potential instability of string vacuum would inducespontaneous breakdown of Lorentz symmetry.One direction in the study of Lorentz violation is to regard Lorentz symmetrybreaking as a possible extension of the standard model in particle physics. In thispaper, we study corrections to quantum electrodynamics modified by twodimension-five LV operatorsΨγμbν’FμνΨå'ŒÎ¨Î³Î¼Î½bF~μνΨin the framework ofeffective field theories.Firstly, the effective polarization and magnetization are identified from themodified Maxwell equations, and the theoretical consequences are investigated. Inaddition, we compute the corrections to the relativistic energy levels of hydrogenatom induced by these Lorentz-violating operators in the absence and presence ofuniform external fields in first-order perturbation theory. We find that the hydrogenspectrum is insensitive to the breakdown of Lorentz boost symmetry. After that, westudy radiative corrections to the extended massless quantum electrodynamics in4dimensional spacetime and in2dimensional spacetime. For the first case, alldivergent one-particle-irreducible Feynman diagrams are calculated at one-loop orderand several related issues are discussed. In particular, it is found that masslessquantum electrodynamics modified by the operator Ψγμb’νFμνΨ alone is one-looprenormalizable. In this context the one-loop Lorentz-violating beta function is derivedand the corresponding running coefficients are obtained. For the other, we calculatethe photon and fermion self-energy Feynman diagrams, and find that these two LVoperators contribute no radiative corrections to self-energy at this order. |
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