Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version accepted for publication in Journal of Physics

The Higgs field and the ultraviolet behaviour of the vortex operator in 2+1 dimensions

We calculate the change in the ultraviolet behaviour of the vortex operator due to the presence of dynamical Higgs field in both 2+1 dimensional QED and the 2+1 dimensional Georgi-Glashow model. We find that in the QED case the presence of the Higgs field leads at the one loop level to power like correction to the propagator of the vortex operator. On the other hand, in the Georgi-Glashow model, the adjoint Higgs at one loop has no affect on the vortex propagator. Thus, as long as the mass of the Higgs field is much larger than the gauge coupling constant, the ultraviolet behaviour of the vortex operator in the Georgi-Glashow model is independent of the Higgs mass.Comment: 14 page

Radius Dependent Luminosity Evolution of Blue Galaxies in GOODS-N

We examine the radius-luminosity (R-L) relation for blue galaxies in the Team Keck Redshift Survey (TKRS) of GOODS-N. We compare with a volume-limited, Sloan Digital Sky Survey sample and find that the R-L relation has evolved to lower surface brightness since z=1. Based on the detection limits of GOODS this can not be explained by incompleteness in low surface-brightness galaxies. Number density arguments rule out a pure radius evolution. It can be explained by a radius dependent decline in B-band luminosity with time. Assuming a linear shift in M_B with z, we use a maximum likelihood method to quantify the evolution. Under these assumptions, large (R_{1/2} > 5 kpc), and intermediate sized (3 < R_{1/2} < 5 kpc) galaxies, have experienced Delta M_B =1.53 (-0.10,+0.13) and 1.65 (-0.18, +0.08) magnitudes of dimming since z=1. A simple exponential decline in star formation with an e-folding time of 3 Gyr can result in this amount of dimming. Meanwhile, small galaxies, or some subset thereof, have experienced more evolution, 2.55 (+/- 0.38) magnitudes. This factor of ten decline in luminosity can be explained by sub-samples of starbursting dwarf systems that fade rapidly, coupled with a decline in burst strength or frequency. Samples of bursting, luminous, blue, compact galaxies at intermediate redshifts have been identified by various previous studies. If there has been some growth in galaxy size with time, these measurements are upper limits on luminosity fading.Comment: 34 Total pages, 15 Written pages, 19 pages of Data Table, 13 Figures, accepted for publication in Ap

Noise thermometry and electron thermometry of a sample-on-cantilever system below 1 Kelvin

We have used two types of thermometry to study thermal fluctuations in a microcantilever-based system below 1 K. We measured the temperature of a cantilever's macroscopic degree-of-freedom (via the Brownian motion of its lowest flexural mode) and its microscopic degrees-of-freedom (via the electron temperature of a metal sample mounted on the cantilever). We also measured both temperatures' response to a localized heat source. We find it possible to maintain thermal equilibrium between these two temperatures and a refrigerator down to at least 300 mK. These results are promising for ongoing experiments to probe quantum effects using micromechanical devices

The Finite Field Kakeya Problem

A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.Comment: 13 page

AEGIS: The color-magnitude relation for X-ray selected AGN

We discuss the relationship between rest-frame color and optical luminosity for X-ray sources in the range 0.6<z<1.4 selected from the Chandra survey of the Extended Groth Strip (EGS). These objects are almost exclusively active galactic nuclei (AGN). While there are a few luminous QSOs, most are relatively weak or obscured AGN whose optical colors should be dominated by host galaxy light. The vast majority of AGN hosts at z~1 are luminous and red, with very few objects fainter than M_{B}=-20.5 or bluer than U-B=0.6. This places the AGN in a distinct region of color-magnitude space, on the ``red sequence'' or at the top of the ``blue cloud'', with many in between these two modes in galaxy color. A key stage in the evolution of massive galaxies is when star formation is quenched, resulting in a migration from the blue cloud to the red sequence. Our results are consistent with scenarios in which AGN either cause or maintain this quenching. The large numbers of red sequence AGN imply that strong, ongoing star formation is not a necessary ingredient for AGN activity, as black hole accretion appears often to persist after star formation has been terminated.Comment: 5 pages, 2 figures, accepted for publication in AEGIS ApJ Letters special editio