Phase Space Representations and Perturbation Theory for Continuous-time Histories

We consider two technical developments of the formalism of continuous-time histories. First, we provide an explicit description of histories of the simple harmonic oscillator on the classical histories phase space, comparing and contrasting the Q, P and Wigner representations; we conclude that a representation based on coherent states is the most appropriate. Second, we demonstrate a generic method for implementing a perturbative approach for interacting theories in the histories formalism, using the quartic anharmonic oscillator. We make use of the identification of the closed-time path (CTP) generating functional with the decoherence functional to develop a perturbative expansion for the latter up to second order in the coupling constant. We consider both configuration space and phase space histories.Comment: 22 pages; slightly shortened, more concise argumentation; ref. adde

The exit-time problem for a Markov jump process

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.Comment: 15 pages, 7 figure

Isolating the Roper Resonance in Lattice QCD

We present results for the first positive parity excited state of the nucleon, namely, the Roper resonance ($N^{{{1/2}}^{+}}$=1440 MeV) from a variational analysis technique. The analysis is performed for pion masses as low as 224 MeV in quenched QCD with the FLIC fermion action. A wide variety of smeared-smeared correlation functions are used to construct correlation matrices. This is done in order to find a suitable basis of operators for the variational analysis such that eigenstates of the QCD Hamiltonian may be isolated. A lower lying Roper state is observed that approaches the physical Roper state. To the best of our knowledge, the first time this state has been identified at light quark masses using a variational approach.Comment: 7pp, 4 figures; minor typos corrected and one Ref. adde

On the Positron Fraction and the Spectrum of the Electronic Component in Cosmic Rays

The recent observations of the positron fraction in cosmic rays by PAMELA indicate that the fraction of positrons to the total electronic component in cosmic rays initially decreases in the energy region 1-10 GeV and increases thereafter. In this paper, we show that it is natural to expect such an increase of the positron fraction within the context of cosmic ray propagation models. It is shown that this ratio should reach an asymptotic value of ~0.6 at very high energies. The specific measurements by PAMELA help us to distinguish amongst various models for cosmic ray propagation, and in particular, they support the nested leaky box model. They also provide, in conjunction with the observations of the total electronic component by HESS, FERMI, ATIC, and other experiments, a way of estimating the spectrum of electrons directly accelerated by discrete sources of cosmic rays in the Galaxy.Comment: 13 Pages, 6 figures; v2: corrected typographical error