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 School webpage.
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”, e-Print: arXiv:1202.1557
Some of my papers about effective actions and their applications in quantum field theory and string theory:
- “Exact computation of one-loop correction to energy of spinning folded string in AdS_5 x S^5”, M. Beccaria, G.V. Dunne, V. Forini, M. Pawellek, A.A. Tseytlin, published in J.Phys.A A43 (2010) 165402 ; e-Print: arXiv:1001.4018 [hep-th]
- “Exact computation of one-loop correction to energy of pulsating strings in AdS5xS5”, M. Beccaria, G.V. Dunne, G. Macorini, A.A. Tseytlin, published in J.Phys.A A44 (2011) 015404 ; arXiv:1009.2318 [hep-th]
- “Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions”, A. Das, G. V. Dunne, published in Phys.Rev. D74 (2006) 044029 ; arXiv:hep-th/0607168v1
- “Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay”, G.V. Dunne, H. Min, published in Phys.Rev. D72 (2005) 125004 ; arXiv:hep-th/0511156
- “Precise quark mass dependence of instanton determinant”, G.V. Dunne, Jin Hur, Choonkyu Lee, H. Min, published in Phys.Rev.Lett. 94 (2005) 072001 ; e-Print: hep-th/0410190
- “Derivative expansion of the effective action and vacuum instability for QED in (2+1)-dimensions”, D. Cangemi, E. D’Hoker, G. V. Dunne, published in Phys.Rev. D51 (1995) 2513-2516 ; arxiv preprint
- “Effective energy for QED in (2+1)-dimensions with semilocalized magnetic fields: A Solvable model”, D. Cangemi, E. D’Hoker, G. V. Dunne, published in Phys.Rev. D52 (1995) 3163-3167 ; arXiv:hep-th/9506085v1
- “An exact (3+1)-dimensional QED effective action”, G. V. Dunne, T. M. Hall , published in Phys.Lett. B419 (1998) 322-325 ; arxiv preprint
- “On the QED effective action in time dependent electric backgrounds”, G. V. Dunne, T. M. Hall , published in Phys.Rev. D58 (1998) 105022 ; arxiv preprint
- “Borel summation of the derivative expansion and effective actions”, G. V. Dunne, T. M. Hall , published in Phys.Rev. D60 (1999) 065002 ; arxiv preprint