In-Out Formalism for Effective Actions in QED and Gravity

by Dr Kim Sang Pyo (Department of Physics, Kunsan National University, Korea)

Friday 10 Jul 2015, 11:30 → 12:30 Europe/Rome

Aula Teorici (Dipartimento di Fisica e Astronomia)

Recently, quantum field theory in strong background fields such as electromagnetic fields or curved spacetimes has raised not only theoretical interest but also experimental interest. Intense lasers, for instance, ELI or IZEST open a window for possible observations of nonperturbative quantum effects, such as the spontaneous pair production from the Dirac sea and the birefringence, photon-photon scattering and photon splitting from the nonlinear vacuum polarization. An intense electromagnetic field or a matter field in a curved spacetime can probe the quantum structure of the Dirac sea or the spacetime. The Schwinger effect and the Hawking radiation have been the most prominent nonperturbative phenomena for many decades. For this purpose one needs quantum field theoretical methods to find the one-loop effective action or the pair-production rate in electromagnetic fields or black holes. More than six decades ago, Schwinger introduced the in-out formalism based on the variational principle, which has been further elaborated by DeWitt. In the in-out formalism, the one-loop effective action is obtained from the scattering matrix between the in-vacuum and the out vacuum, which in turn is expressed in terms of Bogoliubov coefficients. Remarkably, the Bogoliubov coefficients for exactly solvable field theoretical models could be expressed in terms of gamma functions with complex arguments, which lead to one-loop effective actions via the zeta-function regularization. The gamma-function regularization recovers the Heisenberg-Euler and Schwinger one-loop QED action in a constant electromagnetic field and leads to new QED actions in some localized electric or magnetic fields. The one-loop effective action and, more interestingly, QED action are found in an (anti-) de Sitter space. The Schwinger effect and the Hawking radiation compete with each other. The one-loop QED action and the pair production exhibit the strong intertwinement between the Maxwell theory and gravity. Further, there is a gauge-gravity relation for the one-loop action and pair-production rate.

Slides Bologna_SPKIM.pdf