Self-duality, Helicity and Higher-loop Euler-Heisenberg Effective Actions

The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop quantities. This mirrors similar behavior recently found in two-loop amplitudes in N=4 SUSY Yang-Mills theory.Comment: 7 pp, latex, axodraw.sty; Based on talks given by G. Dunne at QTS3 (Cincinnati, OH, Sept. 2003) and QFEXT03 (Norman, OK, Sept. 2003

Pair creation in inhomogeneous fields from worldline instantons

We show how to do semiclassical nonperturbative computations within the worldline approach to quantum field theory using ``worldline instantons''. These worldline instantons are classical solutions to the Euclidean worldline loop equations of motion, and are closed spacetime loops parametrized by the proper-time. Specifically, we compute the imaginary part of the one loop effective action in scalar and spinor QED using worldline instantons, for a wide class of inhomogeneous electric field backgrounds.Comment: 10 pages, 2 figures, talk given by C.S. at X Mexican Workshop on Particles and Fields, Morelia, Mexico, Nov. 6 - 12, 2005 (to appear in the conference proceedings

Electron effective mass in Al0.72_{0.72}Ga0.28_{0.28}N alloys determined by mid-infrared optical Hall effect

The effective electron mass parameter in Si-doped Al$_{0.72}$Ga$_{0.28}$N is determined to be $m^\ast=(0.336\pm0.020)\,m_0$ from mid-infrared optical Hall effect measurements. No significant anisotropy of the effective electron mass parameter is found supporting theoretical predictions. Assuming a linear change of the effective electron mass with the Al content in AlGaN alloys and $m^\ast=0.232\,m_0$ for GaN, an average effective electron mass of $m^\ast=0.376\,m_0$ can be extrapolated for AlN. The analysis of mid-infrared spectroscopic ellipsometry measurements further confirms the two phonon mode behavior of the E$_1$(TO) and one phonon mode behavior of the A$_1$(LO) phonon mode in high-Al-content AlGaN alloys as seen in previous Raman scattering studies

Closed-form two-loop Euler-Heisenberg Lagrangian in a self-dual background

We show that the two-loop Euler-Heisenberg effective Lagrangian for scalar QED in a constant Euclidean self-dual background has a simple explicit closed form expression in terms of the digamma function. This result leads to a simple analysis of the weak- and strong-field expansions, the two-loop scalar QED beta function, and the analytic continuation properties of the effective Lagrangian and its imaginary part.Comment: 8 pages, late

Bernoulli Number Identities from Quantum Field Theory and Topological String Theory

We present a new method for the derivation of convolution identities for finite sums of products of Bernoulli numbers. Our approach is motivated by the role of these identities in quantum field theory and string theory. We first show that the Miki identity and the Faber-Pandharipande-Zagier (FPZ) identity are closely related, and give simple unified proofs which naturally yield a new Bernoulli number convolution identity. We then generalize each of these three identities into new families of convolution identities depending on a continuous parameter. We rederive a cubic generalization of Miki's identity due to Gessel and obtain a new similar identity generalizing the FPZ identity. The generalization of the method to the derivation of convolution identities of arbitrary order is outlined. We also describe an extension to identities which relate convolutions of Euler and Bernoulli numbers.Comment: 18 pages, final version published in CNTP (title modified, note added on relevant work that has appeared since the preprint version; otherwise unchanged

Schwinger Pair Creation of Particles and Strings

I shortly review the worldline instanton method for calculating Schwinger pair production rates in (i) one-loop QED (ii) multiloop QED and (iii) one-loop open string theory.Comment: 8 pages, 3 figures, talk given at XIV Mexican School of Particles and Fields, November 8 - 12, 2010, Morelia, Mexico, to appear in the conference proceeding