Confinement and the analytic structure of the one body propagator in Scalar QED

We investigate the behavior of the one body propagator in SQED. The self energy is calculated using three different methods: i) the simple bubble summation, ii) the Dyson-Schwinger equation, and iii) the Feynman-Schwinger represantation. The Feynman-Schwinger representation allows an {\em exact} analytical result. It is shown that, while the exact result produces a real mass pole for all couplings, the bubble sum and the Dyson-Schwinger approach in rainbow approximation leads to complex mass poles beyond a certain critical coupling. The model exhibits confinement, yet the exact solution still has one body propagators with {\it real} mass poles.Comment: 5 pages 2 figures, accepted for publication in Phys. Rev.

Covariant equations for the three-body bound state

The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including the Wigner rotations and rho-spin decomposition of the off-shell particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative rho-spin states of the off-shell particle.Comment: 57 pages, RevTeX, 6 figures, uses epsf.st

Gauging the three-nucleon spectator equation

We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound state electromagnetic current, as well as the transition currents for the scattering processes \gamma He3 -> NNN, Nd -> \gamma Nd, and \gamma He3 -> Nd. As a result, a unified covariant three-dimensional description of the NNN-\gamma NNN system is achieved.Comment: 23 pages, REVTeX, epsf, 4 Postscript figure

The value of improved (ERS) information based on domestic distribution effects of U.S. agriculture crops

The value of improving information for forecasting future crop harvests was investigated. Emphasis was placed upon establishing practical evaluation procedures firmly based in economic theory. The analysis was applied to the case of U.S. domestic wheat consumption. Estimates for a cost of storage function and a demand function for wheat were calculated. A model of market determinations of wheat inventories was developed for inventory adjustment. The carry-over horizon is computed by the solution of a nonlinear programming problem, and related variables such as spot and future price at each stage are determined. The model is adaptable to other markets. Results are shown to depend critically on the accuracy of current and proposed measurement techniques. The quantitative results are presented parametrically, in terms of various possible values of current and future accuracies

The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures

Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical mechanics especially its key quantity, entropy. Whereas in conventional thermostatistics, the homogeneity and extensivity of the system and the concavity of its entropy are central conditions, these fail for the systems considered here. For example, at phase separation, the entropy, S(E), is necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as inhomogeneities and surface effects cannot be scaled away, one must be careful with the standard arguments of splitting a system into two subsystems, or bringing two systems into thermal contact with energy or particle exchange. Not only the volume part of the entropy must be considered. As will be shown here, when removing constraints in regions of a negative heat capacity, the system may even relax under a flow of heat (energy) against a temperature slope. Thus the Clausius formulation of the second law: ``Heat always flows from hot to cold'', can be violated. Temperature is not a necessary or fundamental control parameter of thermostatistics. However, the second law is still satisfied and the total Boltzmann entropy increases. In the final sections of this paper, the general microscopic mechanism leading to condensation and to the convexity of the microcanonical entropy at phase separation is sketched. Also the microscopic conditions for the existence (or non-existence) of a critical end-point of the phase-separation are discussed. This is explained for the liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of Chemical Physic

Permutable entire functions satisfying algebraic differential equations

It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.Comment: 5 page

Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

Conference Discussion of the Nuclear Force

Discussion of the nuclear force, lead by a round table consisting of T. Cohen, E. Epelbaum, R. Machleidt, and F. Gross (chair). After an invited talk by Machleidt, published elsewhere in these proceedings, brief remarks are made by Epelbaum, Cohen, and Gross, followed by discussion from the floor moderated by the chair. The chair asked the round table and the participants to focus on the following issues: (i) What does each approach (chiral effective field theory, large Nc, and relativistic phenomenology) contribute to our knowledge of the nuclear force? Do we need them all? Is any one transcendent? (ii) How important for applications (few body, nuclear structure, EMC effect, for example) are precise fits to the NN data below 350 MeV? How precise do these fits have to be? (iii) Can we learn anything about nonperturbative QCD from these studies of the nuclear force? The discussion presented here is based on a video recording made at the conference and transcribed afterward.Comment: Discussion at the 21st European Conference on Few Body Problems (EFP21) held at Salamanca, Spain, 30 Aug - 3 Sept 201

Enhancement of kinetic energy fluctuations due to expansion

Global equilibrium fragmentation inside a freeze out constraining volume is a working hypothesis widely used in nuclear fragmentation statistical models. In the framework of classical Lennard Jones molecular dynamics, we study how the relaxation of the fixed volume constraint affects the posterior evolution of microscopic correlations, and how a non-confined fragmentation scenario is established. A study of the dynamical evolution of the relative kinetic energy fluctuations was also performed. We found that asymptotic measurements of such observable can be related to the number of decaying channels available to the system at fragmentation time.Comment: 6 pages, 4 figure