Asymptotic states and renormalization in Lorentz-violating quantum field theory

Abstract

Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension (SME) are studied at linear order in Lorentz breakdown. It is found that the spinor kinetic operator, and thus the free-particle physics, is modified by Lorentz-violating operators absent from the original Lagrangian. As a consequence of this result, both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted. The necessary adaptations are worked out explicitly at first order in Lorentz-breaking coefficients.

26 pages two-column REVTeX, 5 figures, pole extraction clarified, matches published version

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• Unitarity in Maxwell-Carroll-Field-Jackiw electrodynamics
• Covariant Quantization of CPT-violating Photons
• Searching for CPT Violation with Neutral-Meson Oscillations
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• Cherenkov Radiation with Massive, CPT-violating Photons
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• From classical Lagrangians to Hamilton operators in the Standard-Model Extension
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• Beta-Decay Spectrum and Lorentz Violation
• Decays $Z\to \gamma \gamma$ and $Z\to gg$ in the Standard Model Extension
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• Constraining dimension-six nonminimal Lorentz-violating electron-nucleon interactions with EDM physics
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• Lorentz violation parameters and noncommutative scale
• Asymptotic single-particle states and exact Lorentz-violating all-loop quantum corrections for scalar field theory
• Lorentz and CPT Tests using Penning Traps
• Are inertial vacua equivalent in Lorentz-violating theories? Does it matter?
• Lorentz Symmetry Violation in QCD and the Frustration of Asymptotic Freedom
• Constraining EDM and MDM lepton dimension five interactions in the electroweak sector