Using the Hopf Algebra Structure of QFT in Calculations

We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum electrodynamics in four dimensions.Comment: 28 p, Revtex, epsf for figures, minor changes, to appear in Phys.Rev.

Fast Evaluation of Feynman Diagrams

We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based on based on the theory of generalized sinc ($\sin(x)/x$) functions, from which we derive an approximation to the propagator that is expressed as an infinite sum. When the propagators in the Feynman integrals are replaced with the approximate form all integrals over internal momenta and vertices are converted into Gaussians, which can be evaluated analytically. Performing the Gaussians yields a multi-dimensional infinite sum which approximates the corresponding Feynman integral. The difference between the exact result and this approximation is set by an adjustable parameter, and can be made arbitrarily small. We discuss the extraction of regularization independent quantities and demonstrate, both in theory and practice, that these sums can be evaluated quickly, even for third or fourth order diagrams. Lastly, we survey strategies for numerically evaluating the multi-dimensional sums. We illustrate the method with specific examples, including the the second order sunset diagram from quartic scalar field theory, and several higher-order diagrams. In this initial paper we focus upon scalar field theories in Euclidean spacetime, but expect that this approach can be generalized to fields with spin.Comment: uses feynmp macros; v2 contains improved description of renormalization, plus other minor change

Free-form lens model and mass estimation of the high redshift galaxy cluster ACT-CL J0102-4915, "El Gordo"

We examine the massive colliding cluster El Gordo, one of the most massive clusters at high redshift. We use a free-form lensing reconstruction method that avoids making assumptions about the mass distribution. We use data from the RELICS program and identify new multiply lensed system candidates. The new set of constraints and free-form method provides a new independent mass estimate of this intriguing colliding cluster. Our results are found to be consistent with earlier parametric models, indirectly confirming the assumptions made in earlier work. By fitting a double gNFW profile to the lens model, and extrapolating to the virial radius, we infer a total mass for the cluster of $M_{200c}=(1.08^{+0.65}_{-0.12})\times10^{15}$M$_{\odot}$. We estimate the uncertainty in the mass due to errors in the photometric redshifts, and discuss the uncertainty in the inferred virial mass due to the extrapolation from the lens model. We also find in our lens map a mass overdensity corresponding to the large cometary tail of hot gas, reinforcing its interpretation as a large tidal feature predicted by hydrodynamical simulations that mimic El Gordo. Finally, we discuss the observed relation between the plasma and the mass map, finding that the peak in the projected mass map may be associated with a large concentration of colder gas, exhibiting possible star formation. El Gordo is one of the first clusters that will be observed with JWST, which is expected to unveil new high redshift lensed galaxies around this interesting cluster, and provide a more accurate estimation of its mass.Comment: 19 pages, 10 figures. Updated figure

The redshift of the gravitationally lensed radio source PKS1830-211

We report on the spectroscopic identification and the long awaited redshift measurement of the heavily obscured, gravitationally lensed radio source PKS 1830-211, which was first observed as a radio Einstein ring. The NE component of the doubly imaged core is identified, in our infrared spectrum covering the wavelength range 1.5-2.5 microns, as an impressively reddened quasar at z=2.507. Our redshift measurement, together with the recently measured time delay (Lovell et al.), means that we are a step closer to determining the Hubble constant from this lens. Converting the time delay into the Hubble constant by using existing models leads to high values for the Hubble constant. Since the lensing galaxy lies very close to the center of the lensed ring, improving the error bars on the Hubble constant will require not only a more precise time delay measurement, but also very precise astrometry of the whole system.Comment: 11 pages, 2 figures, Accepted ApJ

Large-scale structure in a new deep IRAS galaxy redshift survey

We present here the first results from two recently completed, fully sampled redshift surveys comprising 3703 IRAS Faint Source Survey (FSS) galaxies. An unbiased counts-in-cells analysis finds a clustering strength in broad agreement with other recent redshift surveys and at odds with the standard cold dark matter model. We combine our data with those from the QDOT and 1.2 Jy surveys, producing a single estimate of the IRAS galaxy clustering strength. We compare the data with the power spectrum derived from a mixed dark matter universe. Direct comparison of the clustering strength seen in the IRAS samples with that seen in the APM-Stromlo survey suggests b_O/b_I=1.20+/-0.05 assuming a linear, scale independent biasing. We also perform a cell by cell comparison of our FSS-z sample with galaxies from the first CfA slice, testing the viability of a linear-biasing scheme linking the two. We are able to rule out models in which the FSS-z galaxies identically trace the CfA galaxies on scales 5-20h^{-1}Mpc. On scales of 5 and 10h^{-1}Mpc no linear-biasing model can be found relating the two samples. We argue that this result is expected since the CfA sample includes more elliptical galaxies which have different clustering properties from spirals. On scales of 20h^{-1}Mpc no linear-biasing model with b_O/b_I < 1.70 is acceptable. When comparing the FSS-z galaxies to the CfA spirals, however, the two populations trace the same structures within our uncertaintie

Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page

Galactic periodicity and the oscillating G model

We consider the model involving the oscillation of the effective gravitational constant that has been put forward in an attempt to reconcile the observed periodicity in the galaxy number distribution with the standard cosmological models. This model involves a highly nonlinear dynamics which we analyze numerically. We carry out a detailed study of the bound that nucleosynthesis imposes on this model. The analysis shows that for any assumed value for $\Omega$ (the total energy density) one can fix the value of $\Omega_{\rm bar}$ (the baryonic energy density) in such a way as to accommodate the observational constraints coming from the $^4{\rm He}$ primordial abundance. In particular, if we impose the inflationary value $\Omega=1$ the resulting baryonic energy density turns out to be $\Omega_{\rm bar}\sim 0.021$. This result lies in the very narrow range $0.016 \leq \Omega_{\rm bar} \leq 0.026$ allowed by the observed values of the primordial abundances of the other light elements. The remaining fraction of $\Omega$ corresponds to dark matter represented by a scalar field.Comment: Latex file 29 pages with no figures. Please contact M.Salgado for figures. A more careful study of the model appears in gr-qc/960603

The static quark-antiquark potential in QCD to three loops

The static potential between an infinitely heavy quark and antiquark is derived in the framework of perturbative QCD to three loops by performing a full calculation of the two-loop diagrams and using the renormalization group. The contribution of massless fermions is included.Comment: Latex, 11 pages, 3 figures included. The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/ . Revised version, essentially identical to the version published in Physical Review Letter