Second quantized scalar field, ; Time-dependent electromagnetic fields, ; Quantum invariants, ; Pair production
Publication Date
2014-12
Journal
ANNALS OF PHYSICS, v.351, pp.54 - 67
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
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.