Non-Hermitian Interactions Between Harmonic Oscillators, with Applications to Stable, Lorentz-Violating QED

We examine a new application of the Holstein-Primakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinite-dimensional representations of the Lie algebra $su(2)$. The representations contain nonstandard raising and lowering operators, which are nonlinearly related to the standard $a^{\dag}$ and $a$. The new operators also give rise to a natural family of two-oscillator couplings. These nonlinear couplings are not generally self-adjoint, but their low-energy limits are self-adjoint, exactly solvable, and stable. We discuss the structure of a theory involving these couplings. Such a theory might have as its ultra-low-energy limit a Lorentz-violating Abelian gauge theory, and we discuss the extremely strong astrophysical constraints on such a model.Comment: 11 page

Eliminating the CPT-Odd f Coefficient from the Lorentz-Violating Standard Model Extension

The fermionic f coefficient in the Lorentz-violating standard model extension presents a puzzle. Thus far, no observable quantity that depends upon f has ever been found. We show that this is because f is actually unnecessary. It has absolutely no effects at leading order and can be completely absorbed into other coefficients of the theory by a redefinition of the field.Comment: 12 page

Limits on Neutron Lorentz Violation from Pulsar Timing

Pulsars are the most accurate naturally occurring clocks, and data about them can be used to set bounds on neutron-sector Lorentz violations. If SO(3) rotation symmetry is completely broken for neutrons, then pulsars' rotation speeds will vary periodically. Pulsar timing data limits the relevant Lorentz-violating coefficients to be smaller than 1.7 x 10^(-8) at at least 90% confidence.Comment: 10 pages, version to appear in Phys. Rev.

Lorentz Violation and Faddeev-Popov Ghosts

We consider how Lorentz-violating interactions in the Faddeev-Popov ghost sector will affect scalar QED. The behavior depends sensitively on whether the gauge symmetry is spontaneously broken. If the symmetry is not broken, Lorentz violations in the ghost sector are unphysical, but if there is spontaneous breaking, radiative corrections will induce Lorentz-violating and gauge-dependent terms in other sectors of the theory.Comment: 13 page