Teaching the hidden symmetry of the Kepler problem in relativistic quantum mechanics - from Pauli to Dirac electron

Hidden symmetry in Coulomb interaction is one of the mysterious problems of modern physics. Additional conserved quantities associated with extra symmetry govern wide variety of physics problems, from planetary motion till fine and hyperfine structures of atomic spectra. In this paper we present a simple derivation of hidden symmetry operator in relativistic quantum mechanics for the Dirac equation in the Coulomb field. We established that this operator may be reduced to the one introduced by Johnson and Lippmann. It is worthwhile to notice that this operator was discussed in literature very rarely and so is not known well among physicists and was omitted even in the recent textbooks on relativistic quantum mechanics and/or quantum electrodynamics.Comment: 5 page

Quantum Electrodynamics of the Helium Atom

Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and radiative corrections to the Schr"odinger energy. Average values of these operators can be calculated using a variational Schr"odinger wave function.Comment: 23 pages, revte

National Strength and Conditioning Association position statement on weightlifting for sports performance

The origins of weightlifting and feats of strength span back to ancient Egypt, China, and Greece, with the introduction of weightlifting into the Olympic Games in 1896. However, it was not until the 1950s that training based on weightlifting was adopted by strength coaches working with team sports and athletics, with weightlifting research in peer-reviewed journals becoming prominent since the 1970s. Over the past few decades, researchers have focused on the use of weightlifting-based training to enhance performance in nonweightlifters because of the biomechanical similarities (e.g., rapid forceful extension of the hips, knees, and ankles) associated with the second pull phase of the clean and snatch, the drive/thrust phase of the jerk and athletic tasks such as jumping and sprinting. The highest force, rate of force development, and power outputs have been reported during such movements, highlighting the potential for such tasks to enhance these key physical qualities in athletes. In addition, the ability to manipulate barbell load across the extensive range of weightlifting exercises and their derivatives permits the strength and conditioning coach the opportunity to emphasize the development of strength-speed and speed-strength, as required for the individual athlete. As such, the results of numerous longitudinal studies and subsequent meta-analyses demonstrate the inclusion of weightlifting exercises into strength and conditioning programs results in greater improvements in force-production characteristics and performance in athletic tasks than general resistance training or plyometric training alone. However, it is essential that such exercises are appropriately programmed adopting a sequential approach across training blocks (including exercise variation, loads, and volumes) to ensure the desired adaptations, whereas strength and conditioning coaches emphasize appropriate technique and skill development of athletes performing such exercises

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

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

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

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

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.