A Matrix Model for QCD: QCD Colour is Mixed

We use general arguments to show that coloured QCD states when restricted to gauge invariant local observables are mixed. This result has important implications for confinement: a pure colourless state can never evolve into two coloured states by unitary evolution. Furthermore, the mean energy in such a mixed coloured state is infinite. Our arguments are confirmed in a matrix model for QCD that we have developed using the work of Narasimhan and Ramadas and Singer. This model, a $(0+1)$-dimensional quantum mechanical model for gluons free of divergences and capturing important topological aspects of QCD, is adapted to analytical and numerical work. It is also suitable to work on large $N$ QCD. As applications, we show that the gluon spectrum is gapped and also estimate some low-lying levels for $N=2$ and 3 (colors). Incidentally the considerations here are generic and apply to any non-abelian gauge theory.Comment: 16 pages, 3 figures. V2: comments regarding infinite energy and confinement adde

Spontaneous Breaking of Lorentz Symmetry and Vertex Operators for Vortices

We first review the spontaneous Lorentz symmetry breaking in the presence of massless gauge fields and infraparticles. This result was obtained long time ago in the context of rigorious quantum field theory by Frohlich et. al. and reformulated by Balachandran and Vaidya using the notion of superselection sectors and direction-dependent test functions at spatial infinity for the non-local observables. Inspired by these developments and under the assumption that the spectrum of the electric charge is quantized, (in units of a fundamental charge e) we construct a family of vertex operators which create winding number k, electrically charged Abelian vortices from the vacuum (zero winding number sector) and/or shift the winding number by k units. In particular, we find that for rotating vortices the vertex operator at level k shifts the angular momentum of the vortex by k \frac{{\tilde q}}{q}, where \tilde q is the electric charge of the quantum state of the vortex and q is the charge of the vortex scalar field under the U(1) gauge field. We also show that, for charged-particle-vortex composites angular momentum eigenvalues shift by k \frac{{\tilde q}}{q}, {\tilde q} being the electric charge of the charged-particle-vortex composite. This leads to the result that for \frac{{\tilde q}}{q} half-odd integral and for odd k our vertex operators flip the statistics of charged-particle-vortex composites from bosons to fermions and vice versa. For fractional values of \frac{{\tilde q}}{q}, application of vertex operator on charged-particle-vortex composite leads in general to composites with anyonic statistics.Comment: Published version, 15+1 pages, 1 figur

Novel Edge States in Self-Dual Gravity

In contrast to the Einstein-Hilbert action, the action for self-dual gravity contains vierbeins. They are eleminated at the level of observables by an $SL(2,\mathbb{C})$ gauge condition implied by the action. We argue that despite this condition, new "edge" or superselected state vectors corresponding to maps of the spheres $S^2_{\infty}$ at infinity to $SL(2, \mathbb{C})$ arise. They are characterised by new quantum numbers and they lead to mixed states. For black holes, they arise both at the horizon and the spatial infinity and may be relevant for the black hole information paradox. Similar comments can be made about the Einstein-Palatini action which uses vierbeins.Comment: 15 pages, reference added, some minor notational changes - no changes in conclusio

Magnetic Domains and Surface Effects in Hollow Maghemite Nanoparticles

In the present work, we investigate the magnetic properties of ferrimagnetic and noninteracting maghemite (g-Fe2O3) hollow nanoparticles obtained by the Kirkendall effect. From the experimental characterization of their magnetic behavior, we find that polycrystalline hollow maghemite nanoparticles are characterized by low superparamagnetic-to-ferromagnetic transition temperatures, small magnetic moments, significant coercivities and irreversibility fields, and no magnetic saturation on external magnetic fields up to 5 T. These results are interpreted in terms of the microstructural parameters characterizing the maghemite shells by means of an atomistic Monte Carlo simulation of an individual spherical shell model. The model comprises strongly interacting crystallographic domains arranged in a spherical shell with random orientations and anisotropy axis. The Monte Carlo simulation allows discernment between the influence of the structure polycrystalline and its hollow geometry, while revealing the magnetic domain arrangement in the different temperature regimes.Comment: 26 pages, 8 figures. In press in Phys. Rev.

Pensions and Intertemporal Choice: Evidence from the U.S. Military

SSRN-id2383874We study a choice made by over 20,000 U.S. military personnel annually between the High-3 and Redux retirement plans. Compared to High-3, Redux offers a $30,000 current lump sum payment in exchange for lower future annuity payments. Despite break-even discount rates between 10chose Redux. The likelihood of choosing Redux is decreasing with the break-even discount rate and is related to individual demographics. The implied personal discount rates from this choice are around 9.2Offering this choice has already saved the government over$2 billion in future retirement payments