Non-Hermitian Interactions Between Harmonic Oscillators, with Applications to Stable, Lorentz-Violating QED
arXiv:hep-th/0402036 · doi:10.1063/1.2159070
Abstract
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 . The representations contain nonstandard raising and lowering operators, which are nonlinearly related to the standard and . 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.
11 pages
References in corpus (18)
- Lorentz-Violating Extension of the Standard Model
- CPT Violation and the Standard Model
- Gravity, Lorentz Violation, and the Standard Model
- High-Energy Tests of Lorentz Invariance
- Signals for Lorentz Violation in Electrodynamics
- Stability, Causality, and Lorentz and CPT Violation
- Radiatively Induced Lorentz and CPT Violation in Electrodynamics
- Cosmological Constraints on Lorentz Violation in Electrodynamics
- One-Loop Renormalization of Lorentz-Violating Electrodynamics
- Exact calculation of the radiatively-induced Lorentz and CPT violation in QED
- Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics
- Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics
- Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED
- Magnetic monopoles with generalized quantization condition
- Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential
- New non-unitary representations in a Dirac hydrogen atom
- Microcausality and Energy-Positivity in all frames imply Lorentz Invariance of dispersion laws
- Infinitesimally Nonlocal Lorentz Violation