Quantum field dynamics of the slow rollover in the linear delta expansion

We show how the linear delta expansion, as applied to the slow-roll transition in quantum mechanics, can be recast in the closed time-path formalism. This results in simpler, explicit expressions than were obtained in the Schr\"odinger formulation and allows for a straightforward generalization to higher dimensions. Motivated by the success of the method in the quantum-mechanical problem, where it has been shown to give more accurate results for longer than existing alternatives, we apply the linear delta expansion to four-dimensional field theory. At small times all methods agree. At later times, the first-order linear delta expansion is consistently higher that Hartree-Fock, but does not show any sign of a turnover. A turnover emerges in second-order of the method, but the value of $$at the turnover is larger that that given by the Hartree-Fock approximation. Based on this calculation, and our experience in the corresponding quantum-mechanical problem, we believe that the Hartree-Fock approximation does indeed underestimate the value of$$ at the turnover. In subsequent applications of the method we hope to implement the calculation in the context of an expanding universe, following the line of earlier calculations by Boyanovsky {\sl et al.}, who used the Hartree-Fock and large-N methods. It seems clear, however, that the method will become unreliable as the system enters the reheating stage.Comment: 17 pages, 9 figures, revised version with extra section 4.2 including second order calculatio

Dimensional Reduction in Non-Supersymmetric Theories

It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.Comment: 13 pages, phyzzx, LTH 32

Mound Laboratory Progress Report for December 1963

MOUND LABORATORY PROGRESS REPORT FOR DECEMBER 1963. Has been deleted because of its length

MOUND LABORATORY PROGRESS REPORT FOR JULY 1963

8 7 6 2 ; 7 4 7 6 : 7 8 : : ; half life of 3.781 plus or minus 0.010 years based on calorimetric measuiements. The calorimetric assay of the sample will be continued ior several years to decrease the probable error. The decay scheme for /sup 209/Po--/sup 209/Po/ isitopic mixtures is being determined. The gamma spectrum is being studied using two sources of different isotopic composition. Definite peaks were established at 76, 260, 300, 575, and 9l0 kev. Various multiple coincidence experiments indicated that the 300- and 575-kev photons and the 76-kev x-ray are in triple coincidence. Relative intensities of the various gamma rays from the two different sources indicated that the 575-kev photon is associated with /sup 208/ Po decay, while the 260- and 910-kev states are attributed to /sup 209/Po. A theoretical estimate of the partial alpha half life for /sup 208/Po decay to the 2+ level in /sup 204/Pb (at 0.899 Mev) was made. This value (2.5 x 10/sup 6/ years) was determined graphically by extrapolation to an alpha particle energy of 4.2l1 Mev. /sup 209/Po--/sup 2o9/Po sources are being prepared for the investigation of the internal conversion electron spectra of these isotopes. Ion exchange techniques are being studied for the separation of /sup 227/Ac from / sup 227/Th, /sup 223/R a, and /sup 226/Ra. Naturally occurring lanthanum, thorium, and barium are being used as experimental substitutes. Composite elution curves indicated that lanthanum and /sup 232/Th can be successfully isolated with 2 M HCl, 3 M HNO/sub 3/, and ammonium acetate as elutrients. A purified form of the original Dowex 50W-X8 column packing matenial was used; the new material (AG-50W-X8) reduced tailing on the elution curves. /sup 228/Th was tentatively assigned a half life of 1.9132 years with an internal probable error of 0.0005 year. The presence of /sup 210/Po and actinium must be positively identified in the sample by chemical analysis and alpha pulse height analyses. Mound Laboratory is studying the separation and purification of /sup 234/U from aged /sup 238/Pu using ion exchange and solvent extraction techniques. A batch containing an estimated 250 milligrams of /sup 234/U in 26.2 grams of plutonium is being processed. The anion exchange separation procedure for this batch was completed. More than 99% of the plutonium was removed from the uranium. A spectrophotometric method is being developed for the determination of /sup 234/ U in samples containing aluminum, iron, and plutonium. The extraneous metallic ions were separated, and the uranium was complexed with 1-(2-pyridylazo)-2- naphthol (PAN). After the color developed, the absorbance was read at 570 m mu . Standard uranium samples were analyzed, and Beer's law was followed between 0 and 80 mu g of uranium. Gram quantities of over 90% pure /sup 13/C are being prepared. Various thermal diffusion column configurations are being used for separation efficiency studies and evaluation of feed gases, such as carbon monoxide or methane. The first five stages of the seven-stage cascade system of hot-wire and concentrictube columns are enriching natural methane to about 23% / sup 13/C while coming to steady state conditions. The concertric tube columns enriched methane from 60 to over 90% /sup 13/C in the total carbon. About 1.5 grams of product containing about 10% impurities were accumulated. The use of alternating current for heating thermal diffusion column wires is being studied. Vibration of the wire is the major problem. Two parallel iron discs were used to align the electrical leads and the column wire in the pool of mercury; however, the discs did not prevent vibration. The mercury pool was replaced by rubber bands, and subsequently by a spring, for tensioning the wire; there was a slight vibration. A braided cable was used as an electrical lead for alternating current and as a vibration damper. Both the vibration and the use of a mercury pool were eliminated. An integral was set up to determine the error introduced into the calibration o

In-situ velocity imaging of ultracold atoms using slow--light

The optical response of a moving medium suitably driven into a slow-light propagation regime strongly depends on its velocity. This effect can be used to devise a novel scheme for imaging ultraslow velocity fields. The scheme turns out to be particularly amenable to study in-situ the dynamics of collective and topological excitations of a trapped Bose-Einstein condensate. We illustrate the advantages of using slow-light imaging specifically for sloshing oscillations and bent vortices in a stirred condensate

Clarifying Some Remaining Questions in the Anomaly Puzzle

We discuss several points that may help to clarify some questions that remain about the anomaly puzzle in supersymmetric theories. In particular, we consider a general N=1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way to put the R-current and the stress tensor in a single supercurrent, even though in the classical theory they are in the same supermultiplet. As is well known, the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents in 4-dimensional spacetime, namely the supercurrent that has the energy-momentum tensor as one of its components. This expression for the lowest component is an energy-dependent linear combination of two chiral currents, which itself does not correspond to a classically conserved chiral current. The lowest component of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen theorem. The lowest component of the first supercurrent has an anomaly that we show is consistent with the anomaly of the trace of the energy-momentum tensor. Therefore, we conclude that there is no consistent way to put the R-current and the stress tensor in a single supercurrent in the quantized theory. We also discuss and try to clarify some technical points in the derivations of the two-supercurrents in the literature. These latter points concern the significance of infrared contributions to the NSVZ beta-function and the role of the equations of motion in deriving the two supercurrents.Comment: 22 pages, no figure. v2: minor changes. v3: sections re-organized. new subsections (IVA, IVB) added. references adde

Transport in Coupled Quantum Dots: Kondo Effect Versus Anti-Ferromagnetic Correlation

The interplay between the Kondo effect and the inter-dot magnetic interaction in a coupled-dot system is studied. An exact result for the transport properties at zero temperature is obtained by diagonalizing a cluster, composed by the double-dot and its vicinity, which is connected to leads. It is shown that the system goes continuously from the Kondo regime to an anti-ferromagnetic state as the inter-dot interaction is increased. The conductance, the charge at the dots and the spin-spin correlation are obtained as a function of the gate potential.Comment: 4 pages, 3 postscript figures. Submitted to PR

The Fayet-Iliopoulos D-term and its renormalisation in softly-broken supersymmetric theories

We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken abelian supersymmetric theory, and calculate the associated beta-function through three loops. We show that there exists (at least through three loops) a renormalisation group invariant trajectory for the coefficient of the D-term, corresponding to the conformal anomaly solution for the soft masses and couplings.Comment: 30 pages, Revtex, 15 Figures. Minor changes, and inadvertent omission of author from this abstract correcte

Factorization of integrals, defining the beta-function, into integrals of total derivatives in N=1 SQED, regularized by higher derivatives

Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics in all orders.Comment: 14 page