Abstract
In this paper, we give formal results of Schwinger pair production correction in thermal systems with external background field by using the evolution operator method of thermo field dynamics, where especially tree level correction of thermal photons is considered with linear response approaches by an effective mass shift. We consider initial systems in two types of vacuums as zero temperature and thermal vacuum, respectively, with correction of thermal photons is or not included. As an example we give results of these corrections to pair production for a constant external background electric field.
Highlights
In an early work of Schwinger, it is shown that a very strong constant electric field decays to real charged pairs [1]
Assuming that thermal fields are turned off when t → ∞ and employing semiclassical mass shift mÃ2 1⁄4 m2 − q2hAγ;μAγμi to reflect the corrections of thermal photon fields, we find that Tγ appears in the exponent, which decreases the threshold of tunneling so that it enhances the rate of pair production
Note that when UðAexÞ acts on the vacuum the result depends on the asymptotic structure of the vacuum, and so does UðθÞ. This means that in order to take the tree-level correction of thermal photons into pair production, we only need to do a mass shift in the Bogoliubov coefficient, so the threshold has gone down (EÃ− 1⁄4 2mÃ−c2 < 2mc2), which verifies our guess that the dressing of thermal photons enhances pair production
Summary
In an early work of Schwinger, it is shown that a very strong constant electric field decays to real charged pairs [1]. [5,6,7,8,9,10], prove that the thermal effect enhances pair production These indicate that there is a temperature threshold Tc 1⁄4 qE=2πm [7] and discrete resonant peaks TÃ 1⁄4 nqE=2πm [9] in a constant electric field E, where q and m are charge and mass. In general thermal QED systems, the thermal photons are present and usually are considered in loop corrections but ignored in tree-level calculations We notice that they influence the structure of vacuum, affecting the result of pair production. To obtain a measurable pair production rate at finite temperature, and to make a distinction among thermal charged particles, thermal photons, and external electromagnetic fields, we use the operator method of thermofield dynamics (TFD), adding an effective mass shift approach. The charge and the mass of boson and fermion have unified marks as q and m
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