String Organization of Field Theories: Duality and Gauge Invariance

String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invariant while expressions for single diagrams are not.Comment: 20 pages in Latex, including seven figures in postscrip

Formation and evolution of coronal rain observed by SDO/AIA on February 22, 2012

The formation and dynamics of coronal rain are currently not fully understood. Coronal rain is the fall of cool and dense blobs formed by thermal instability in the solar corona towards the solar surface with acceleration smaller than gravitational free fall. We aim to study the observational evidence of the formation of coronal rain and to trace the detailed dynamics of individual blobs. We used time series of the 171 \AA\, and 304 \AA\, spectral lines obtained by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) above active region AR 11420 on February 22, 2012. Observations show that a coronal loop disappeared in the 171 \AA\ channel and appeared in the 304 \AA\ line$\text{}\text{}$ more than one hour later, which indicates a rapid cooling of the coronal loop from 1 MK to 0.05 MK. An energy estimation shows that the radiation is higher than the heat input, which indicates so-called catastrophic cooling. The cooling was accompanied by the formation of coronal rain in the form of falling cold plasma. We studied two different sequences of falling blobs. The first sequence includes three different blobs. The mean velocities of the blobs were estimated to be 50 km s$^{-1}$, 60 km s$^{-1}$ and 40 km s$^{-1}$. A polynomial fit shows the different values of the acceleration for different blobs, which are lower than free-fall in the solar corona. The first and second blob move along the same path, but with and without acceleration, respectively. We performed simple numerical simulations for two consecutive blobs, which show that the second blob moves in a medium that is modified by the passage of the first blob. Therefore, the second blob has a relatively high speed and no acceleration, as is shown by observations. The second sequence includes two different blobs with mean velocities of 100 km s$^{-1}$ and 90 km s$^{-1}$, respectively.Comment: 8 pages, 8 figures, Accepted in A&

Quasi-oscillatory dynamics observed in ascending phase of the flare on March 6, 2012

Context. The dynamics of the flaring loops in active region (AR) 11429 are studied. The observed dynamics consist of several evolution stages of the flaring loop system during both the ascending and descending phases of the registered M-class flare. The dynamical properties can also be classified by different types of magnetic reconnection, related plasma ejection and aperiodic flows, quasi-periodic oscillatory motions, and rapid temperature and density changes, among others. The focus of the present paper is on a specific time interval during the ascending (pre-flare) phase. Aims. The goal is to understand the quasi-periodic behavior in both space and time of the magnetic loop structures during the considered time interval. Methods.We have studied the characteristic location, motion, and periodicity properties of the flaring loops by examining space-time diagrams and intensity variation analysis along the coronal magnetic loops using AIA intensity and HMI magnetogram images (from the Solar Dynamics Observatory(SDO)). Results. We detected bright plasma blobs along the coronal loop during the ascending phase of the solar flare, the intensity variations of which clearly show quasi-periodic behavior. We also determined the periods of these oscillations. Conclusions. Two different interpretations are presented for the observed dynamics. Firstly, the oscillations are interpreted as the manifestation of non-fundamental harmonics of longitudinal standing acoustic oscillations driven by the thermodynamically nonequilibrium background (with time variable density and temperature). The second possible interpretation we provide is that the observed bright blobs could be a signature of a strongly twisted coronal loop that is kink unstable.Comment: 12 pages, 10 figures, A&A, in pres

A New Approach for Analytic Amplitude Calculations

We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz scalars. The new approach renders the symbolic calculation of some complicated physical processes more feasible and easier, especially with the assistance of algebra manipulating codes for computer.Comment: LaTex, no figure, to appear in PR

Long-period oscillations of active region patterns: least-squares mapping on second-order curves

Active regions (ARs) are the main sources of variety in solar dynamic events. Automated detection and identification tools need to be developed for solar features for a deeper understanding of the solar cycle. Of particular interest here are the dynamical properties of the ARs, regardless of their internal structure and sunspot distribution. We studied the oscillatory dynamics of two ARs: NOAA 11327 and NOAA 11726 using two different methods of pattern recognition. We developed a novel method of automated AR border detection and compared it to an existing method for the proof-of-concept. The first method uses least-squares fitting on the smallest ellipse enclosing the AR, while the second method applies regression on the convex hull.} After processing the data, we found that the axes and the inclination angle of the ellipse and the convex hull oscillate in time. These oscillations are interpreted as the second harmonic of the standing long-period kink oscillations (with the node at the apex) of the magnetic flux tube connecting the two main sunspots of the ARs. In both ARs we have estimated the distribution of the phase speed magnitude along the magnetic tubes (along the two main spots) by interpreting the obtained oscillation of the inclination angle as the standing second harmonic kink mode. After comparing the obtained results for fast and slow kink modes, we conclude that both of these modes are good candidates to explain the observed oscillations of the AR inclination angles, as in the high plasma $\beta$ regime the phase speeds of these modes are comparable and on the order of the Alfv\'{e}n speed. Based on the properties of the observed oscillations, we detected the appropriate depth of the sunspot patterns, which coincides with estimations made by helioseismic methods. The latter analysis can be used as a basis for developing a magneto-seismological tool for ARs.Comment: 10 pages, 6 figures, Accepted for publication in A&

Multigluon Helicity Amplitudes Involving a Quark Loop

We apply the solution to the recursion relation for the double-off-shell quark current to the problem of computing one loop amplitudes with an arbitrary number of gluons. We are able to compute amplitudes for photon-gluon scattering, electron-positron annihilation to gluons, and gluon-gluon scattering via a quark loop in the case of like-helicity gluons. In addition, we present the result for the one-loop gluon-gluon scattering amplitude when one of the gluons has opposite helicity from the others.Comment: 31 pages (RevTeX) + 2 uuencoded figures (included), Fermilab-Pub-93/389-

Inelastic J/ψJ/\psi production in polarized photon-hadron collisions

Presented here is a calculation of inelastic $J/\psi$ production in polarized photon-hadron collisions under the framework of NRQCD factorization formalism. We consider the photoproduction of \jpsi in the energy range relevant to HERA. The Weizs\"acker-Williams approximation is adopted in the evaluation of the cross sections for $ep$ collisions. We found that this process can give another independent test for the color-octet mechanism, and the different features for the two color-octet processes may provide further informations on the mechanism for inelastic \jpsi photoproduction. And the discrepancy on the production asymmetry $A$ between various sets of polarized gluon distribution functions is also found to be distinctive.Comment: 14pages, 6 PS figure

One Loop Multiphoton Helicity Amplitudes

We use the solutions to the recursion relations for double-off-shell fermion currents to compute helicity amplitudes for $n$-photon scattering and electron-positron annihilation to photons in the massless limit of QED. The form of these solutions is simple enough to allow {\it all}\ of the integrations to be performed explicitly. For $n$-photon scattering, we find that unless $n=4$, the amplitudes for the helicity configurations (+++...+) and (-++...+) vanish to one-loop order.Comment: 27 pages + 4 uuencoded figures (included), Fermilab-Pub-93/327-T, RevTe

Weyl-van-der-Waerden formalism for helicity amplitudes of massive particles

The Weyl-van-der-Waerden spinor technique for calculating helicity amplitudes of massive and massless particles is presented in a form that is particularly well suited to a direct implementation in computer algebra. Moreover, we explain how to exploit discrete symmetries and how to avoid unphysical poles in amplitudes in practice. The efficiency of the formalism is demonstrated by giving explicit compact results for the helicity amplitudes of the processes gamma gamma -> f fbar, f fbar -> gamma gamma gamma, mu^- mu^+ -> f fbar gamma.Comment: 24 pages, late

Diffractive light quark jet production at hadron colliders in the two-gluon exchange model

Massless quark and antiquark jet production at large transverse momentum in the coherent diffractive processes at hadron colliders is calculated in the two-gluon exchange parametrization of the Pomeron model. We use the helicity amplitude method to calculate the cross section formula. We find that for the light quark jet production the diffractive process is related to the differential off-diagonal gluon distribution function in the proton. We estimate the production rate for this process at the Fermilab Tevatron by approximating the off-diagonal gluon distribution function by the usual diagonal gluon distribution in the proton. And we find that the cross sections for the diffractive light quark jet production and the charm quark jet production are in the same order of magnitude. We also use the helicity amplitude method to calculate the diffractive charm jet production at hadron colliders, by which we reproduce the leading logarithmic approximation result of this process we previously calculated.Comment: 15 pages, 4 PS figures, Revte