Second Quantized Scalar QED in Homogeneous Time-Dependent Electromagnetic Fields
Abstract
We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.
Keywords
Cite
@article{arxiv.1403.6263,
title = {Second Quantized Scalar QED in Homogeneous Time-Dependent Electromagnetic Fields},
author = {Sang Pyo Kim},
journal= {arXiv preprint arXiv:1403.6263},
year = {2015}
}
Comments
RevTex 12 pages, no figure; replaced by the version to be published in Ann. Phys