The quantum vacuum is unstable under the influence of an external electric field, as the virtual electron-positron dipole pairs can gain energy from the external field. If the field is sufficiently strong, these virtual particles can gain the threshold pair creation energy 2mc^2 and become real electron-positron pairs. This remarkable phenomenon was first predicted by Heisenberg and his student Hans Euler in 1936, based on work of Sauter in 1931, and later formalized in the language of QED by Schwinger in 1951. However, the electric field required to see this effect is astronomically huge, E_critical~ 10^(16) V/cm, and so it has not yet been directly observed, even using the strongest lasers.

Theoretically, this is a non-perturbative effect, as the virtual particles tunnel out of the Dirac sea. This makes this elusive effect of great interest for other theories, such as quantum chromodynamics (QCD), where non-perturbative effects are known to be significant but are not directly accessible, and also in gravitational physics, in particular for the phenomena of Hawking radiation near a black hole, and Unruh radiation of accelerating mirrors. It is also closely related to the dynamical Casimir effect of atomic physics.

Several large laser facilities [ELI, XFEL, HIPER] are coming tantalizingly close to the required electric field strength, which necessitates a re-thinking of the observability of the Schwinger effect. This has led recently to a fruitful interaction between theorists and experimentalists from high energy physics, laser physics, plasma physics, fusion physics, and accelerator physics, to develop ways to see the Schwinger effect for the first time.

For a review article from a * Topical issue: Fundamental Physics and Ultra-High Laser Fields * in Eur. Phys. Journ. D., see:

* G. V. Dunne, “New Strong-Field QED Effects at ELI: Nonperturbative Vacuum Pair Production”: arXiv:0812.3163 [hep-th] , Eur.Phys.J. D55 (2009) 327-340

A review article on Heisenberg-Euler effective actions is in the Ian Kogan Memorial Collection: *From Fields to Strings: Circumnavigating Theoretical Physics’*:

* G. V. Dunne, “Heisenberg-Euler effective Lagrangians: Basics and extensions”, arXiv:hep-th/0406216 , in M. Shifman (ed.) et al.: From fields to strings, vol. 1* 445-522

A more historical review article on the Heisenberg-Euler effective action, in honor of the 75th anniversary of its publication, is based on a review talk given at QFEXT11:

* G. V. Dunne, “The Heisenberg-Euler Effective Action: 75 years on”, arXiv:1202.1557

My research has focused recently on accurate theoretical computations of the expected electron-positron production rate, and momentum spectrum, for the electric fields generated in realistic laser pulses. This has led to several new ideas and methods:

**Worldline Instantons**

Christian Schubert [Universidad Michoacana, Mexico] and I proposed a new approach to the Schwinger effect for inhomogeneous electric fields, based on a semiclassical approximation to Feynman’s worldline path integral expression for the effective action. This “worldline instanton” method has the advantage that, unlike other methods such as WKB or the quantum kinetic approach, it has potential to be applied to cases where the field is inhomogeneous in more than one space-time coordinate. This idea has now been developed in various directions in a series of papers with a number of students, postdocs and collaborators:

* G. V. Dunne, C. Schubert, “Worldline instantons and pair production in inhomogenous fields”: arXiv:hep-th/0507174 , Phys.Rev.D72:105004,2005

* G. V. Dunne, H. Gies, C. Schubert and Q. Wang, “Worldline Instantons II: The Fluctuation Prefactor”, arXiv:hep-th/0602176 , Phys.Rev.D73:065028,2006

* G. V. Dunne, Q. Wang, “Multidimensional Worldline Instantons”, arXiv:hep-th/0608020 , Phys.Rev.D74:065015,2006

* D. D. Dietrich, G. V. Dunne, “Gutzwiller’s trace formula and vacuum pair production”, arXiv:0706.4006 [hep-th] , J.Phys.A A40 (2007) F825-F830

* C. K. Dumlu, G. V. Dunne, “Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production”, arXiv:1110.1657 [hep-th], Phys.Rev.D84:125023, 2011

**Dynamically Assisted Schwinger Mechanism**

With Ralf Schuetzhold [Univ. Duisberg-Essen] and Holger Gies [Univ. Jena], we proposed a way to enhance the pair production effect by combining a stronger slower pulse [such as from an optical laser] with a faster weaker pulse [such as from an X-ray laser], leading surprisingly to an exponential enhancement. Physically, the faster pulse gives a multi-photon contribution which reduces the barrier the electron has to tunnel through, with tunneling governed by the slower pulse. Hence the exponential enhancement. Explicit experimental realizations have been proposed — see for example: A. Di Piazza, E. Lotstedt, A.I. Milstein, C.H. Keitel, “Barrier control in tunneling e+ – e- photoproduction”, arXiv:0906.0726 [hep-ph] , Phys.Rev.Lett. 103 (2009) 170403.

* R. Schuetzhold, H. Gies, G. Dunne, “Dynamically assisted Schwinger mechanism”, arXiv:0807.0754 [hep-th] , Phys. Rev. Lett. 101, 130404 (2008)

* G. V. Dunne, H. Gies, R. Schuetzhold, “Catalysis of Schwinger Vacuum Pair Production”, arXiv:0908.0948 [hep-ph] , Phys.Rev. D80 (2009) 111301

**Quantum Interference Effects in the Momentum Spectrum for Shaped Laser Pulses**

With a student F. Hebenstreit [Univ. Graz], together with R. Alkofer [Graz] and H. Gies [Jena], we found numerical evidence of strong interference effects in the momentum spectrum of the produced electron-positron pairs. This can be used both as an enhancement and as a diagnostic tool. The effect is exactly out-of-phase between scalar and spinor QED, emphasizing the physics of quantum interference as the underlying cause. The semiclassical interpretation and computation was done with my UConn student, Cesim Dumlu, in a series of papers, using various WKB techniques, keeping track of phases interference terms that illustrate the Stokes phenomenon, the fact that WKB solutions are only local, whereas pair production computations require global information. A coherent enhancement mechanism that provides an explicit time-domain realization of the multiple-slit interference phenomenon is proposed in a recent paper with Eric Akkermans, based on an analogy with the Ramsey effect of atomic physics.

* F. Hebenstreit, R. Alkofer, G. V. Dunne, H. Gies, “Momentum signatures for Schwinger pair production in short laser pulses with sub-cycle structure”: arXiv:0901.2631 [hep-ph] , Phys.Rev.Lett. 102 (2009) 150404

* F. Hebenstreit, R. Alkofer, G. V. Dunne, H. Gies, “Quantum statistics effect in Schwinger pair production in short laser pulses”: arXiv:0910.4457 [hep-ph] , in Proceedings of QFXET09, Edited by K.A. Milton, M. Bordag, World Scientific, 2010, Int. J. Mod. Phys. A25 (2010) 2171-2408

* C. K. Dumlu, G. V. Dunne, “The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses”, arXiv:1004.2509 [hep-th] , Phys.Rev.Lett. 104 (2010) 250402

* C. K. Dumlu, G. V. Dunne, “Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses”, arXiv:1102.2899 [hep-th] , Phys.Rev. D83 (2011) 065028

* E. Akkermans, G. V. Dunne, “Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum”, arXiv:1109.3489 [hep-th] , PhysRevLett.108:030401, 2012