Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods

Relativistic methods for the Foldy-Wouthuysen transformation of the ``step-by-step'' type already at the first step give an expression for the Hamilton operator not coinciding with the exact result determined by the Eriksen method. The methods agree for the zeroth and first orders in the Planck constant terms but do not agree for the second and higher-order terms. We analyze the benefits and drawbacks of various methods and establish their applicability boundaries.Comment: 20 page

The Most Technologically Progressive Decade of the Century

Because of the Depression’s place in both the popular and academic imagination, and the repeated and justifiable emphasis on output that was not produced, income that was not earned, and expenditure that did not take place, it will seem startling to propose the following hypothesis: the years 1929–1941 were, in the aggregate, the most technologically progressive of any comparable period in U.S. economic history.1 The hypothesis entails two primary claims: that during this period businesses and government contractors implemented or adopted on a more widespread basis a wide range of new technologies and practices, resulting in the highest rate of measured peacetime peak-to-peak multifactor productivity growth in the century, and secondly, that the Depression years produced advances that replenished and expanded the larder of unexploited or only partially exploited techniques, thus providing the basis for much of the labor and multifactor productivity improvement of the 1950’s and 1960’s

U.S. Economic Growth in the Gilded Age

In the immediate postwar period, Moses Abramovitz and Robert Solow both examined data on output and input growth from the first half of the twentieth century and reached similar conclusions. In the twentieth century, in contrast with the nineteenth, a much smaller fraction of real output growth could be swept back to the growth of inputs conventionally measured. The rise of the residual, they suggested, was an important distinguishing feature of twentieth century growth. This paper identifies two difficulties with this claim. First, TFP growth virtually disappeared in the U.S. between 1973 and 1995. Second, TFP growth was in fact quite robust between the end of the Civil War and 1906, as was in fact acknowledged by Abramovitz in his 1993 EHA Presidential address. Developing a revised macroeconomic narrative is essential in reconciling our interpretation of these numbers with what we know about scientific, technological, and organizational change during the gilded age

Corrections for a constant radial magnetic field in the g-2 and electric-dipole-moment experiments with muons in storage rings

We calculate the corrections for constant radial magnetic field in muon g--2 and electric-dipole-moment experiments in storage rings. While the correction is negligible for the current generation of g--2 experiments, it affects the upcoming muon electric-dipole-moment experiment at Fermilab.Comment: 8 page

Economic Growth and Recovery in the United States, 1919-1941

The first part of this chapter provides an overview of what lay behind record productivity growth in the US economy between 1929 and 1941. The second part considers the role of rigidities and other negative supply conditions in worsening the downturn and slowing recovery. While arguing consistently that the overarching explanation of the Great Depression will and should continue to emphasise a collapse and slow revival in the growth of aggregate demand, the chapter spends relatively little time on what drives this. The emphasis of the chapter is on aggregate supply—both the broad array of positive shocks that propelled potential and, eventually, actual output forward, and the negative conditions which, in interaction with aggregate demand, may have increased the size of the output gap and prolonged its persistence. An appendix offers discussion and updated calculations of productivity growth rates for the critical period 1929–41

Equation of spin motion in storage rings in a cylindrical coordinate system

The exact equation of spin motion in a cylindrical coordinate system with allowance for electric dipole moments of particles has been derived. This equation is convenient for analytical calculations of spin dynamics in circular storage rings when the configuration of main fields is simple enough. The generalized formula for the influence of a vertical betatron oscillation on the angular velocity of spin rotation has been found. This formula agrees with the previously obtained result and contains an additional oscillatory term that can be used for fitting. The relative importance of terms in the equation of spin motion is discussed.Comment: 14 page