Quality Upgrading and its Welfare Cost in U.S. Steel Imports, 1969-74

In this paper we measure the quality change which has occurred in U.S. steel imports during the 1969-74 VRA, using an index number method. Under this approach, the yearly changes in unit values is broken into three components: a quality-adjusted or pure price index; a quality index, which measures changes in the product mix; and a supplier index, which measures changes in the source of supply. We also derive a measure of welfare cost, which equals the inverse of a Paasche price index minus the inverse of an exact price index. Over the 1969-74 VRA period we find quality upgrading of 7.4 percent in U.S. steel imports, which occurs most strongly in the first year. The welfare cost of quality change varies around one percent of import expenditure during 1970-73. This cost is at least as large as the conventional deadweight loss triangle, but smaller than the transfer of quota rents.

Community Service Learning Is a Foregone Conclusion at the Lincoln Elementary School

For the staff at Lincoln Elementary School in Springfield, Massachusetts, articulating the many ways in which community service learning affects their school is nearly impossible. The principal says he doesn\u27t require people to do community service. Yet, on any given day, students all over the school are learning through service projects

Symmetries and Mass Splittings in QCD2_2 Coupled to Adjoint Fermions

Two dimensional QCD coupled to fermions in the adjoint representation of the gauge group $SU(N)$, a useful toy model of QCD strings, is supersymmetric for a certain ratio of quark mass and gauge coupling constant. Here we study the theory in the vicinity of the supersymmetric point; in particular we exhibit the algebraic structure of the model and show that the mass splittings as one moves away from the supersymmetric point obey a universal relation of the form ${M_i}^2(B)-{M_i}^2(F)=M_i\delta m+O(\delta m^3)$. We discuss the connection of this relation to string and quark model expectations and verify it numerically for large $N$. At least for low lying states the $O(\delta m^3)$ corrections are extremely small. We also discuss a natural generalization of QCD$_2$ with an infinite number of couplings, which preserves SUSY. This leads to a Landau -- Ginzburg description of the theory, and may be useful for defining a scaling limit in which smooth worldsheets appear.Comment: 16 pages + 3 figures available upon request, harvmac, EFI-93-6

Modular Invariance, Finiteness, and Misaligned Supersymmetry: New Constraints on the Numbers of Physical String States

We investigate the generic distribution of bosonic and fermionic states at all mass levels in non-supersymmetric string theories, and find that a hidden ``misaligned supersymmetry'' must always appear in the string spectrum. We show that this misaligned supersymmetry is ultimately responsible for the finiteness of string amplitudes in the absence of full spacetime supersymmetry, and therefore the existence of misaligned supersymmetry provides a natural constraint on the degree to which spacetime supersymmetry can be broken in string theory without destroying the finiteness of string amplitudes. Misaligned supersymmetry also explains how the requirements of modular invariance and absence of physical tachyons generically affect the distribution of states throughout the string spectrum, and implicitly furnishes a two-variable generalization of some well-known results in the theory of modular functions.Comment: standard LaTeX; 55 pages, 4 figures. (Note: This replaced version matches the version which was published in Nuclear Physics B.

Absence of Physical Walls in Hot Gauge Theories

This paper shows that there are no {\em physical} walls in the deconfined, high-temperature phase of $Z(2)$ lattice gauge theory. In a Hamiltonian formulation, the interface in the Wilson lines is not physical. The line interface and its energy are interpreted in terms of physical variables. They are associated with a difference between two partition functions. One includes only the configurations with even flux across the interface. The other is restricted to odd flux. Also, with matter present, there is no physical metastable state. However, the free energy is lowered by the matter. This effect is described in terms of physical variables.Comment: 25 pages, Revte

Studies of the Potential Curve Crossing Problem I. Analysis of Stueckelberg\u27s Method

A detailed critical analysis is made of Stueckelberg\u27s treatment of inelastic transitions at a crossing of two potential curves. Using an asymptotic method analogous to the WKB approximation, Stueckelberg obtained the well-known Landau-Zener-Stueckelberg (LZS) formula for the inelastic transition probability. His method involved the determination of connection formulas linking amplitudes associated with his asymptotic approximants on either side of the crossing-point region. Here we show that (a) Stueckelberg\u27s asymptotic approximants are just the WKB approximants for elastic scattering on the adiabatic (noncrossing) potential curves; (b) Stueckelberg\u27s method for obtaining the connection formulas can be put on a rigorous footing, including sufficient conditions for its validity, using the classical trajectory equations derivable from a general semiclassical theory of inelastic atomic collisions; (c) there is an undetermined phase in the S matrix, which Stueckelberg incorrectly assumed to be zero, and which has the value 14π in the distorted-wave approximation; (d) Stueckelberg\u27s derivation is not valid whenever the inelastic transition probability is small, either in the rapid-passage (diabatic) case or the near-adiabatic limit; (e) for realistic model parameters, the conditions needed for Stueckelberg\u27s derivation to be valid are almost never satisfied. Since the LZS formula is known from numerical computations to be valid under some conditions when the Stueckelberg derivation is not valid, we conclude that analysis via connection-formula methods is not a useful technique for treating the crossing problem. In an appendix we derive an analytical result for the Stokes\u27s constants determining the Stueckelberg connection formulas. The result is an absolutely convergent, infinite series whose numerical evaluation would yield exactly the unknown phase associated with the LZS formula

Large NN Solution of the 2D Supersymmetric Yang-Mills Theory

The Schwinger-Dyson equations of the Makeenko-Migdal type, when supplemented with some simple equations as consequence of supersymmetry, form a closed set of equations for Wilson loops and related quantities in the two dimensional super-gauge theory. We solve these equations. It appears that the planar Wilson loops are described by the Nambu string without folds. We also discuss how to put the model on a spatial lattice, where a peculiar gauge is chosen in order to keep one supersymmetry on the lattice. Supersymmetry is unbroken in this theory. We comment on possible generalization of these considerations to other models.Comment: 22 pages, 5 figures included, harvma

Universality in Two Dimensional Gauge Theory.

We discuss two dimensional Yang -- Mills theories with massless fermions in arbitrary representations of a gauge group $G$. It is shown that the physics (spectrum and interactions) of the massive states in such models is independent of the detailed structure of the model, and only depends on the gauge group $G$ and an integer $k$ measuring the total anomaly. The massless physics, which does depend on the details of the model, decouples (almost) completely from that of the massive one. As an example, we discuss the equivalence of QCD$_2$ coupled to fermions in the adjoint, and fundamental representations.Comment: 16 pages, harvma

The Perils of `Soft' SUSY Breaking

We consider a two dimensional SU(N) gauge theory coupled to an adjoint Majorana fermion, which is known to be supersymmetric for a particular value of fermion mass. We investigate the `soft' supersymmetry breaking of the discrete light cone quantization (DLCQ) of this theory. There are several DLCQ formulations of this theory currently in the literature and they naively appear to behave differently under `soft' supersymmetry breaking at finite resolution. We show that all these formulations nevertheless yield identical bound state masses in the decompactification limit of the light-like circle. Moreover, we are able to show that the supersymmetry-inspired version of DLCQ (so called `SDLCQ') provides the best rate of convergence of DLCQ bound state masses towards the actual continuum values, except possibly near or at the critical fermion mass. In this last case, we discuss improved extrapolation schemes that must supplement the DLCQ algorithm in order to obtain correct continuum bound state masses. Interestingly, when we truncate the Fock space to two particles, the SDLCQ prescription presented here provides a scheme for improving the rate of convergence of the massive t'Hooft model. Thus the supersymmetry-inspired SDLCQ prescription is applicable to theories without supersymmetry.Comment: 11 pages, Latex; 2 figures (EPS); Numerical results extended; conclusions revise