Reconsidered estimates of the 10th order QED contributions to the muon anomaly

The problem of estimating the 10th order QED corrections to the muon anomalous magnetic moment is reconsidered. The incorporation of the recently improved contributions to the $\alpha^4$ and $\alpha^5$- corrections to $a_{\mu}$ within the renormalization-group inspired scheme-invariant approach leads to the estimate $a_{\mu}^{(10)}\approx 643(\alpha/pi)^5$. It is in good agreement with the estimate $a_{\mu}^{(10)}= 663(20) (\alpha/\pi)^5$, obtained by Kinoshita and Nio from the numerical calculations of 2958 10-th order diagrams, which are considered to be more important than the still uncalculated 6122 10th-order $m_{\mu}/m_e$-dependent vertex graphs, and 12672 5-loop diagrams, responsible for the mass-independent constant contribution both to $a_{\mu}$ and $a_e$. This confirms Kinoshita and Nio guess about dominance of the 10-th order diagrams calculated by them. Comparisons with other estimates of the $\alpha^5$- contributions to $a_{\mu}$, which exist in the literature, are presented.Comment: 19 pages, LaTeX, some misprints in the text and literature corrected. Results unchaged, to appear in Phys.Rev.

Supersymmetry and the Chiral Schwinger Model

We have constructed the N=1/2 supersymmetric general Abelian model with asymmetric chiral couplings. This leads to a N=1/2 supersymmetrization of the Schwinger model. We show that the supersymmetric general model is plagued with problems of infrared divergence. Only the supersymmetric chiral Schwinger model is free from such problems and is dynamically equivalent to the chiral Schwinger model because of the peculiar structure of the N=1/2 multiplets.Comment: one 9 pages Latex file, one ps file with one figur

Particle Spectrum Created Through Bubble Nucleation

Using the multi-dimensional wave function formalism, we investigate the quantum state of a scalar field inside a true vacuum bubble nucleated through false vacuum decay in flat spacetime. We developed a formalism which allows us a mode-by-mode analysis. To demonstrate its advantage, we describe in detail the evolution of the quantum state during the tunneling process in terms of individual mode functions and interpret the result in the language of particle creation. The spectrum of the created particles is examined based on quantum field theory in the Milne universe.Comment: 14 pages, revtex file, 4 uuencoded compressed postscript figures appended at the en

Hadronic Loop Corrections to the Muon Anomalous Magnetic Moment

The dominant theoretical uncertainties in both, the anomalous magnetic moment of the muon and the value of the electromagnetic coupling at the Z scale arise from their hadronic contributions. Since these will ultimately dominate the experimental errors, we study the correlation between them, as well as with other fundamental parameters. To this end we present analytical formulas for the QCD contribution from higher energies and from heavy quarks. Including these correlations affects the Higgs boson mass extracted from precision data.Comment: 4 page

Exact Effective Action for (1+1 Dimensional) Fermions in an Abelian Background at Finite Temperature

In an effort to further understand the structure of effective actions for fermions in an external gauge background at finite temperature, we study the example of 1+1 dimensional fermions interacting with an arbitrary Abelian gauge field. We evaluate the effective action exactly at finite temperature. This effective action is non-analytic as is expected at finite temperature. However, contrary to the structure at zero temperature and contrary to naive expectations, the effective action at finite temperature has interactions to all (even) orders (which, however, do not lead to any quantum corrections). The covariant structure thus obtained may prove useful in studying 2+1 dimensional models in arbitrary backgrounds. We also comment briefly on the solubility of various 1+1 dimensional models at finite temperature.Comment: A few clarifying remarks added;21 page

Testing new physics with the electron g-2

We argue that the anomalous magnetic moment of the electron (a_e) can be used to probe new physics. We show that the present bound on new-physics contributions to a_e is 8*10^-13, but the sensitivity can be improved by about an order of magnitude with new measurements of a_e and more refined determinations of alpha in atomic-physics experiments. Tests on new-physics effects in a_e can play a crucial role in the interpretation of the observed discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large class of models, new contributions to magnetic moments scale with the square of lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in which this scaling is violated and larger effects in a_e are expected. In such models the value of a_e is correlated with specific predictions for processes with violation of lepton number or lepton universality, and with the electric dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde

Sea-Level Rise: Projections for Maryland 2018

In fulfillment of requirements of the Maryland Commission on Climate Change Act of 2015, this report provides updated projections of the amount of sea-level rise relative to Maryland coastal lands that is expected into the next century. These projections represent the consensus of an Expert Group drawn from the Mid-Atlantic region. The framework for these projections is explicitly tied to the projections of global sea-level rise included in the Intergovernmental Panel on Climate Change Fifth Assessment (2014) and incorporates regional factors such as subsidence, distance from melting glaciers and polar ice sheets, and ocean currents. The probability distribution of estimates of relative sea-level rise from the baseline year of 2000 are provided over time and, after 2050, for three different greenhouse gas emissions pathways: Growing Emissions (RCP8.5), Stabilized Emissions (RCP4.5), and meeting the Paris Agreement (RCP2.6). This framework has been recently used in developing relative sea-level rise projections for California, Oregon, Washington, New Jersey, and Delaware as well as several metropolitan areas. The Likely range (66% probability) of the relative rise of mean sea level expected in Maryland between 2000 and 2050 is 0.8 to 1.6 feet, with about a one-in-twenty chance it could exceed 2.0 feet and about a one-in-one hundred chance it could exceed 2.3 feet. Later this century, rates of sea-level rise increasingly depend on the future pathway of global emissions of greenhouse gases during the next sixty years. If emissions continue to grow well into the second half of the 21st century, the Likely range of sea-level rise experienced in Maryland is 2.0 to 4.2 feet over this century, two to four times the sea-level rise experienced during the 20th century. Moreover, there is a one-in-twenty chance that it could exceed 5.2 feet. If, on the other hand, global society were able to bring net greenhouse gas emissions to zero in time to meet the goals of the Paris Climate Agreement and reduce emissions sufficient to limit the increase in global mean temperature to less than 2Celsius over pre-industrial levels, the Likely range for 2100 is 1.2 to 3.0 feet, with a one-in-twenty chance that it would exceed 3.7 feet. The difference in sea-level rise between these contrasting scenarios would diverge even more during the next century, with the failure to reduce emissions in the near term resulting in much greater sea-level rise 100 years from now. Moreover, recent research suggests that, without imminent and substantial reductions in greenhouse gas emissions, the loss of polar ice sheets-and thus the rate of sea-level rise-may be more rapid than assumed in these projections, particularly under the Growing Emissions scenario. These probabilistic sea-level rise projections can and should be used in planning and regulation, infrastructure siting and design, estimation of changes in tidal range and storm surge, developing inundation mapping tools, and adaptation strategies for high-tide flooding and saltwater intrusion

From Euler's play with infinite series to the anomalous magnetic moment

During a first St. Petersburg period Leonhard Euler, in his early twenties, became interested in the Basel problem: summing the series of inverse squares (posed by Pietro Mengoli in mid 17th century). In the words of Andre Weil (1989) "as with most questions that ever attracted his attention, he never abandoned it". Euler introduced on the way the alternating "phi-series", the better converging companion of the zeta function, the first example of a polylogarithm at a root of unity. He realized - empirically! - that odd zeta values appear to be new (transcendental?) numbers. It is amazing to see how, a quarter of a millennium later, the numbers Euler played with, "however repugnant" this game might have seemed to his contemporary lovers of the "higher kind of calculus", reappeared in the analytic calculation of the anomalous magnetic moment of the electron, the most precisely calculated and measured physical quantity. Mathematicians, inspired by ideas of Grothendieck, are reviving the dream of Galois of uncovering a group structure in the ring of periods (that includes the multiple zeta values) - applied to the study of Feynman amplitudes.Comment: v.2: minor corrections, references adde

The mechanism of spin and charge separation in one dimensional quantum antiferromagnets

We reconsider the problem of separation of spin and charge in one dimensional quantum antiferromagnets. We show that spin and charge separation in one dimensional strongly correlated systems cannot be described by the slave boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations which carry the separate spin and charge quantum numbers are solitons. To prove this {\it no-go} result, it is sufficient to study the pure spinon sector in the slave boson representation. We start with a short-range RVB spin liquid mean-field theory for the frustrated antiferromagnetic spin-${1\over2}$ chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations non-perturbatively.Comment: 53 pages; Revtex 3.

Effect of transition layers on the electromagnetic properties of composites containing conducting fibres

The approach to calculating the effective dielectric and magnetic response in bounded composite materials is developed. The method is essentially based on the renormalisation of the dielectric matrix parameters to account for the surface polarisation and the displacement currents at the interfaces. This makes it possible the use of the effective medium theory developed for unbounded materials, where the spatially-dependent local dielectric constant and magnetic permeability are introduced. A detailed mathematical analysis is given for a dielectric layer having conducting fibres with in-plane positions. The surface effects are most essential at microwave frequencies in correspondence to the resonance excitation of fibres. In thin layers (having a thickness of the transition layer), the effective dielectric constant has a dispersion region at much higher frequencies compared to those for unbounded materials, exhibiting a strong dependence on the layer thickness. For the geometry considered, the effective magnetic permeability differs slightly from unity and corresponds to the renormalised matrix parameter. The magnetic effect is due entirely to the existence of the surface displacement currents.Comment: PDF, 33 pages, 10 figure