Perturbation theory for the two-dimensional abelian Higgs model in the unitary gauge

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other hand, it is formally equal to the limit $\xi \to 0$ of the renormalizable R$_{\xi}$-gauge. We consider perturbation theory to one-loop order in the R$_{\xi}$-gauge and in the unitary gauge for the case of the two-dimensional abelian Higgs model. An apparent conflict between the unitary gauge and the limit $\xi \to 0$ of the R$_{\xi}$-gauge is resolved, and it is demonstrated that results for physical quantities can be obtained in the unitary gauge.Comment: 15 pages, LaTeX2e, uses the feynmf package, formulations correcte

Communications Biophysics

Contains reports on three research projects.United States Air Force (Contract AF19(604)-4112

Anisotropy of the Cosmic Neutrino Background

The cosmic neutrino background (CNB) consists of low-energy relic neutrinos which decoupled from the cosmological fluid at a redshift z ~ 10^{10}. Despite being the second-most abundant particles in the universe, direct observation remains a distant challenge. Based on the measured neutrino mass differences, one species of neutrinos may still be relativistic with a thermal distribution characterized by the temperature T ~ 1.9K. We show that the temperature distribution on the sky is anisotropic, much like the photon background, experiencing Sachs-Wolfe and integrated Sachs-Wolfe effects.Comment: 5 pages, 2 figures / updated references, discussion of earlier wor

Spin-dynamics of the low-dimensional magnet (CH3)2NH2CuCl3

Dimethylammonium copper (II) chloride (also known as DMACuCl3 or MCCL) is a low dimensional S=1/2 quantum spin system proposed to be an alternating ferro-antiferromagnetic chain with similar magnitude ferromagnetic (FM) and antiferromagnetic (AFM) exchange interactions. Subsequently, it was shown that the existing bulk measurements could be adequately modeled by considering DMACuCl3 as independent AFM and FM dimer spin pairs. We present here new inelastic neutron scattering measurements of the spin-excitations in single crystals of DMACuCl3. These results show significant quasi-one-dimensional coupling, however the magnetic excitations do not propagate along the expected direction. We observe a band of excitations with a gap of 0.95 meV and a bandwidth of 0.82 meV.Comment: 3 pages, 2 figures included in text, submitted to proceedings of International Conference on Neutron Scattering, December 200

New Upper Limits on the Tau Neutrino Mass from Primordial Helium Considerations

In this paper we reconsider recently derived bounds on $MeV$ tau neutrinos, taking into account previously unaccounted for effects. We find that, assuming that the neutrino life-time is longer than $O(100~sec)$, the constraint $N_{eff}<3.6$ rules out $\nu_{\tau}$ masses in the range $0.5~(MeV)<m_{\nu_\tau}<35~(MeV)$ for Majorana neutrinos and $0.74~(MeV)<m_{\nu_\tau}<35~(MeV)$ for Dirac neutrinos. Given that the present laboratory bound is 35 MeV, our results lower the present bound to $0.5$ and $0.74$ for Majorana and Dirac neutrinos respectively.Comment: 9 pages (2 figures available upon request), UM-AC-93-0

Direct Detection of Warm Dark Matter in the X-ray

We point out a serendipitous link between warm dark matter (WDM) models for structure formation on the one hand and the high sensitivity energy range (1-10 keV) for x-ray photon detection on the Chandra and XMM-Newton observatories on the other. This fortuitous match may provide either a direct detection of the dark matter or exclusion of many candidates. We estimate expected x-ray fluxes from field galaxies and clusters of galaxies if the dark matter halos of these objects are composed of WDM candidate particles with rest masses in the structure formation-preferred range (~1 keV to ~20 keV) and with small radiative decay branches. Existing observations lead us to conclude that for singlet neutrinos (possessing a very small mixing with active neutrinos) to be a viable WDM candidate they must have rest masses < 5 keV in the zero lepton number production mode. Future deeper observations may detect or exclude the entire parameter range for the zero lepton number case, perhaps restricting the viability of singlet neutrino WDM models to those where singlet production is driven by a significant lepton number. The Constellation X project has the capability to detect/exclude singlet neutrino WDM for lepton number values up to 10% of the photon number. We also consider diffuse x-ray background constraints on these scenarios. These same x-ray observations additionally may constrain parameters of active neutrino and gravitino WDM candidates.Comment: 11 pages, 6 figures, replacement to match ApJ versio

Communications Biophysics

Contains reports on four research projects.National Institutes of Health (Grant MH-04737-03)National Science Foundation (Grant G-16526)National Aeronautics and Space Administration (Grant NsG-496

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction expansion, a strictly larger class than primitive invertible substitution sequences). It is known that operators from this family have spectra which are Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of this set tends to $1$ as coupling constant $\lambda$ tends to $0$. Moreover, we also show that at small coupling constant, all gaps allowed by the gap labeling theorem are open and furthermore open linearly with respect to $\lambda$. Additionally, we show that, in the small coupling regime, the density of states measure for an operator in this family is exact dimensional. The dimension of the density of states measure is strictly smaller than the Hausdorff dimension of the spectrum and tends to $1$ as $\lambda$ tends to $0$

First Passage Time Densities in Non-Markovian Models with Subthreshold Oscillations

Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process $x(t)$ and particularly the time after which it will reach a certain level $x_b$. The probability density of this first passage time is expressed as infinite series of integrals over joint probability densities of $x$ and its velocity $\dot{x}$. Approximating higher order terms of this series through the lower order ones leads to closed expressions in the cases of vanishing and moderate correlations between subsequent crossings of $x_b$. For a linear oscillator driven by white or coloured Gaussian noise, which models a resonant neuron, we show that these approximations reproduce the complex structures of the first passage time densities characteristic for the underdamped dynamics, where Markovian approximations (giving monotonous first passage time distribution) fail

Lagrangian Becchi-Rouet-Stora-Tyutin treatment of collective coordinates

The Becchi-Rouet-Stora-Tyutin (BRST) treatment for the quantization of collective coordinates is considered in the Lagrangian formalism. The motion of a particle in a Riemannian manifold is studied in the case when the classical solutions break a non-abelian global invariance of the action. Collective coordinates are introduced, and the resulting gauge theory is quantized in the BRST antifield formalism. The partition function is computed perturbatively to two-loops, and it is shown that the results are independent of gauge-fixing parameters.Comment: LaTeX file, 26 pages, PostScript figures at end of fil