Stability, causality, and Lorentz and CPT violation - art. no. 065008

Stability and causality are investigated for quantum held theories incorpor ating Lorentz and CPT violation. Explicit calculations in the quadratic sec tor of a general renormalizable Lagrangian for a massive fermion reveal tha t no difficulty arises for low energies if the parameters controlling the b reaking are small, but for high energies either energy positivity or microc ausality is violated in some observer frame. However, this can be avoided i f the Lagrangian is the sub-Planck limit of a nonlocal theory with spontane ous Lorentz and CPT violation. Our analysis supports the stability and caus ality of the Lorentz- and CPT-violating standard-model extension that would emerge at low energies from spontaneous breaking in a realistic string the ory.