Effective Actions in Quantum Field Theory and String Theory
The quantum effective action encodes the nonlinear properties of a system due to quantum fluctuations, analogously to how the thermodynamic partition function encodes the effects of thermal fluctuations. The effective action therefore contains valuable information about condensates, currents, correlation functions and expectation values, and hence it is also extremely useful in characterizing symmetry breaking. Technically, the computation of the [one-loop] effective action involves computing the determinant of a differential operator, such as the Dirac or Klein-Gordon operator, and part of my research is concerned with developing new techniques for computing the effective action.
For a review of the Euler-Heisenberg effective action, see: G. V. Dunne,
"Heisenberg-Euler effective Lagrangians: Basics and extensions": Lectures Notes (82 pages), 2004. Dedicated to the memory of Ian Kogan; Published in Ian Kogan Memorial Collection, 'From Fields to Strings: Circumnavigating Theoretical Physics'
M. Shifman et al (ed.) vol. 1* 445-522.
preprint version hep-th/0406216
For a review of functional determinants: "Funtional Determinants in
Quantum Field Theory", lectures at the 2008 Saalburg Physics Summer
School. Lecture notes available at the Saalburg
For a historical review of the Euler-Heisenberg effective action and its subsequent impact, from a special session at QFEXT11, G. V. Dunne, "The Heisenberg-Euler Effective Action: 75 years on",
Some of my papers about effective actions and their applications in quantum field theory and string theory: