Bare and Induced Lorentz and CPT Invariance Violations in QED

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Abstract

We consider QED in a constant axial vector background (\AE ther). Further Lorentz invariance violations (LIV) might occur owing to radiative corrections. The phenomenology of this model is studied, clarifying issues related to the various regularizations employed, with a particular emphasis on the induced photon mass. To this concern, it is shown that in the presence of LIV dimensional regularization may produce a radiatively induced finite photon mass. The possible physical role of the large momentum cutoff is elucidated and the finite temperature radiative corrections are evaluated. Finally, various experimental bounds on the parameters of the model are discussed.

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Stability, Causality, and Lorentz and CPT Violation

Ralf Lehnert, Alan Kostelecky (2000)

Stability and causality are investigated for quantum field theories incorporating Lorentz and CPT violation. Explicit calculations in the quadratic sector of a general renormalizable lagrangian for a massive fermion reveal that no difficulty arises for low energies if the parameters controlling the breaking are small, but for high energies either energy positivity or microcausality is violated in some observer frame. However, this can be avoided if the lagrangian is the sub-Planck limit of a nonlocal theory with spontaneous Lorentz and CPT violation. Our analysis supports the stability and causality of the Lorentz- and CPT-violating standard-model extension that would emerge at low energies from spontaneous breaking in a realistic string theory.

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Ultraviolet modifications of dispersion relations in effective field theory

Robert C. Myers, Maxim Pospelov (2003)

The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies, in some scenarios of quantum gravity. We apply effective field theory to this problem and identify dimension 5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles. Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at 10^{-5}/Mpl.

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Emergent CPT violation from the splitting of Fermi points

F. Klinkhamer, G Volovik (2004)

In a fermionic quantum vacuum, the parameters k_\mu of a CPT-violating Chern-Simons-like action term induced by CPT-violating parameters of the fermionic sector depend on the universality class of the system. As a concrete example, we consider the Dirac Hamiltonian of a massive fermionic quasiparticle and add a particular term with purely-spacelike CPT-violating parameters b_\mu=(0,{\bf b}). A quantum phase transition separates two phases, one with a fully-gapped fermion spectrum and the other with topologically-protected Fermi points (gap nodes). The emergent Chern-Simons ``vector'' k_\mu=(0,{\bf k}) now consists of two parts. The regular part, {\bf k}^{reg}, is an analytic function of |{\bf b}| across the quantum phase transition and may be nonzero due to explicit CPT violation at the fundamental level. The anomalous (nonanalytic) part, {\bf k}^{anom}, comes solely from the Fermi points and is proportional to their splitting. In the context of condensed-matter physics, the quantum phase transition may occur in the region of the BEC-BCS crossover for Cooper pairing in the p-wave channel. For elementary particle physics, the splitting of Fermi points may lead to neutrino oscillations, even if the total electromagnetic Chern-Simons-like term cancels out.