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Register a new userEffective Action of QED in Electric Field Backgrounds
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Authors
Sang Pyo Kim
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We use the evolution operator method to find the one-loop effective action of scalar and spinor QED in electric field backgrounds in terms of the Bogoliubov coefficient between the ingoing and the outgoing vacua. We obtain the exact one-loop effective action for a Sauter-type electric field, E_0 sech^2 (t/tau), and show that the imaginary part correctly yields the vacuum persistence. The renormalized effective action shows the general relation between the vacuum persistence and the total mean number of created pairs for the constant and the Sauter-type electric field.
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We find the Bogoliubov coefficient from the tunneling boundary condition on a charged particle coupled to a static electric field $E_0 sech^2 (z/L)$ and, using the regularization scheme in Phys. Rev. D 78, 105013 (2008), obtain the exact one-loop effective action in scalar and spinor QED. It is shown that the effective action satisfies the general relation between the vacuum persistence and the mean number of produced pairs. We advance an approximation method for general electric fields and show the duality between the space-dependent and time-dependent electric fields of the same form at the leading order of the effective actions.
We advance a novel method for the finite-temperature effective action for nonequilibrium quantum fields and find the QED effective action in time-dependent electric fields, where charged pairs evolve out of equilibrium. The imaginary part of the effective action consists of thermal loops of the Fermi-Dirac or Bose-Einstein distribution for the initial thermal ensemble weighted with factors for vacuum fluctuations. And the real part of the effective action is determined by the mean number of produced pairs, vacuum polarization, and thermal distribution. The mean number of produced pairs is equal to twice the imaginary part. We explicitly find the finite-temperature effective action in a constant electric field.
Some astrophysical objects are supposed to have very strong electromagnetic fields above the critical strength. Quantum fluctuations due to strong electromagnetic fields modify the Maxwell theory and particularly electric fields make the vacuum unstable against pair production of charged particles. We study the strong field effect such as the effective action and the Schwinger pair production in scalar QED.
An interesting class of background field configurations in QED are the O(2)xO(3) symmetric fields. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation, for both scalar and spinor QED. Here we use the recently developed partial-wave-cutoff method for a numerical analysis of both effective actions in the full mass range. In particular, at large mass we are able to match the asymptotic behavior of the physically renormalized effective action against the leading two mass levels of the inverse mass (or heat kernel) expansion. At small mass we obtain good numerical results even in the massless case for the appropriately (unphysically) renormalized effective action after the removal of the chiral anomaly term through a small radial cutoff factor. In particular, we show that the effective action after this removal remains finite in the massless limit, which also provides indirect support for M. Frys hypothesis that the QED effective action in this limit is dominated by the chiral anomaly term.
We introduce classical and quantum antifields in the reparametrization-invariant effective action, and derive a deformed classical master equation.
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