Functional Determinants in Quantum Field Theory

Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional problems, a classical result of Gel'fand and Yaglom dramatically simplifies the problem so that the functional determinant can be computed without computing the spectrum of eigenvalues. Here I report recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators), with applications in quantum field theory.Comment: Plenary talk at QTS5 (Quantum Theory and Symmetries); 16 pp, 2 fig

Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls

We extend our previous results of simplified expressions for functional determinants for radial Schr\"odinger operators to the computation of vacuum energy, or mass corrections, for static but spatially radial backgrounds, and for domain wall configurations. Our method is based on the zeta function approach to the Gel'fand-Yaglom theorem, suitably extended to higher dimensional systems on separable manifolds. We find new expressions that are easy to implement numerically, for both zero and nonzero temperature.Comment: 30 page

Self-DUal SU(3) Chern-Simons Higgs Systems

We explore self-dual Chern-Simons Higgs systems with the local $SU(3)$ and global $U(1)$ symmetries where the matter field lies in the adjoint representation. We show that there are three degenerate vacua of different symmetries and study the unbroken symmetry and particle spectrum in each vacuum. We classify the self-dual configurations into three types and study their properties.Comment: Columbia Preprint CU-TP-635, 19 page

Chern-Simons Solitons, Toda Theories and the Chiral Model

The two-dimensional self-dual Chern--Simons equations are equivalent to the conditions for static, zero-energy solutions of the $(2+1)$-dimensional gauged nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In this paper we classify all finite charge $SU(N)$ solutions by first transforming the self-dual Chern--Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck--Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between the $SU(N)$ Toda and $SU(N)$ chiral model solutions

Tunneling Ionization Rates from Arbitrary Potential Wells

We present a practical numerical technique for calculating tunneling ionization rates from arbitrary 1-D potential wells in the presence of a linear external potential by determining the widths of the resonances in the spectral density, rho(E), adiabatically connected to the field-free bound states. While this technique applies to more general external potentials, we focus on the ionization of electrons from atoms and molecules by DC electric fields, as this has an important and immediate impact on the understanding of the multiphoton ionization of molecules in strong laser fields.Comment: 13 pages, 7 figures, LaTe

Supersymmetric quantum mechanics with nonlocal potentials

We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe that both our model Hamiltonian and its supersymmetric partner may have normalizable zero-energy ground states, in contrast to local models with nonperiodic or periodic potentials.Comment: 4 pages, REVTeX, Minor revisions for clarificatio

Laughlin Wave Function and One-Dimensional Free Fermions

Making use of the well-known phase space reduction in the lowest Landau level(LLL), we show that the Laughlin wave function for the $\nu = {1\over m}$ case can be obtained exactly as a coherent state representation of an one dimensional $(1D)$ wave function. The $1D$ system consists of $m$ copies of free fermions associated with each of the $N$ electrons, confined in a common harmonic well potential. Interestingly, the condition for this exact correspondence is found to incorporate Jain's parton picture. We argue that, this correspondence between the free fermions and quantum Hall effect is due to the mapping of the $1D$ system under consideration, to the Gaussian unitary ensemble in the random matrix theory.Comment: 7 pages, Latex , no figure

The Demand for Military Spending in Egypt

Egypt plays a pivotal role in the security of the Middle East as the doorway to Europe and its military expenditure reflects its involvement in the machinations of such an unstable region, showing considerable variation over the last 40 years. These characteristics make it a particularly interesting case study of the determinants of military spending. This paper specifies and estimates an econometric model of the Egyptian demand for military spending, taking into account important strategic and political factors. Both economic and strategic factors are found to play a role in determining military burden/spending, with clear positive effects of lagged military burden, suggesting some sort of institutional inertia, plus negative output and net exports effects. The strategic effect as a result of the impact of Israel's military burden is mostly positive and significant, though its impact is reduced when the impact of important strategic events are taken into account. The military spending of Egypt's allies Jordan and Syria generally seems to have had no effect on Egypt's spending. These results are consistent over a range of econometric techniques. © 2013 © 2013 Taylor & Francis

New HErschel Multi-wavelength Extragalactic Survey of Edge-on Spirals (NHEMESES)

Edge-on spiral galaxies offer a unique perspective on the vertical structure of spiral disks, both stars and the iconic dark dustlanes. The thickness of these dustlanes can now be resolved for the first time with Herschel in far-infrared and sub-mm emission. We present NHEMESES, an ongoing project that targets 12 edge-on spiral galaxies with the PACS and SPIRE instruments on Herschel. These vertically resolved observations of edge-on spirals will impact on several current topics. First and foremost, these Herschel observations will settle whether or not there is a phase change in the vertical structure of the ISM with disk mass. Previously, a dramatic change in dustlane morphology was observed as in massive disks the dust collapses into a thin lane. If this is the case, the vertical balance between turbulence and gravity dictates the ISM structure and consequently star-formation and related phenomena (spiral arms, bars etc.). We specifically target lower mass nearby edge-ons to complement existing Herschel observations of high-mass edge-on spirals (the HEROES project). Secondly, the combined data-set, together with existing Spitzer observations, will drive a new generation of spiral disk Spectral Energy Distribution models. These model how dust reprocesses starlight to thermal emission but the dust geometry remains the critical unknown. And thirdly, the observations will provide an accurate and unbiased census of the cold dusty structures occasionally seen extending out of the plane of the disk, when backlit by the stellar disk. To illustrate the NHEMESES project, we present early results on NGC 4244 and NGC 891, two well studies examples of a low and high-mass edge-on spiral.Comment: 3 pages, 4 figures, to appear in the proceedings of IAU 284, "The Spectral Energy Distribution of Galaxies", (SED2011), 5-9 September 2011, Preston, UK, editors, R.J. Tuffs & C.C.Popescu (v2 updated metadata