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arXiv · 1403.6263

Second Quantized Scalar QED in Homogeneous Time-Dependent Electromagnetic Fields

Sang Pyo Kim
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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.

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Sang Pyo Kim. 2014-03-25. Second Quantized Scalar QED in Homogeneous Time-Dependent Electromagnetic Fields. https://doi.org/10.1016/j.aop.2014.08.012

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