Slowly decaying classical fields, unitarity, and gauge invariance

In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the field goes to zero. The importance of this point is exposed for the counter-example of low-dimensionally expanding systems. The issues of gauge invariance and of the interpretation of the evolution at intermediate times are also intricately linked to that point.Comment: 8 pages, no figure

The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly

We complete our study of non-Abelian gauge theories in the framework of Epstein-Glaser approach to renormalization theory including in the model an arbitrary number of Dirac Fermions. We consider the consistency of the model up to the third order of the perturbation theory. In the second order we obtain pure group theoretical relations expressing a representation property of the numerical coefficients appearing in the left and right handed components of the interaction Lagrangian. In the third order of the perturbation theory we obtain the the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate

Discovery of a very X-ray luminous galaxy cluster at z=0.89 in the WARPS survey

We report the discovery of the galaxy cluster ClJ1226.9+3332 in the Wide Angle ROSAT Pointed Survey (WARPS). At z=0.888 and L_X=1.1e45 erg/s (0.5-2.0 keV, h_0=0.5) ClJ1226.9+3332 is the most distant X-ray luminous cluster currently known. The mere existence of this system represents a huge problem for Omega_0=1 world models. At the modest (off-axis) resolution of the ROSAT PSPC observation in which the system was detected, ClJ1226.9+3332 appears relaxed; an off-axis HRI observation confirms this impression and rules out significant contamination from point sources. However, in moderately deep optical images (R and I band) the cluster exhibits signs of substructure in its apparent galaxy distribution. A first crude estimate of the velocity dispersion of the cluster galaxies based on six redshifts yields a high value of 1650 km/s, indicative of a very massive cluster and/or the presence of substructure along the line of sight. While a more accurate assessment of the dynamical state of this system requires much better data at both optical and X-ray wavelengths, the high mass of the cluster has already been unambiguously confirmed by a very strong detection of the Sunyaev-Zel'dovich effect in its direction (Joy et al. 2001). Using ClJ1226.9+3332 and ClJ0152.7-1357 (z=0.835), the second-most distant X-ray luminous cluster currently known and also a WARPS discovery, we obtain a first estimate of the cluster X-ray luminosity function at 0.8<z<1.4 and L_X>5e44 erg/s. Using the best currently available data, we find the comoving space density of very distant, massive clusters to be in excellent agreement with the value measured locally (z<0.3), and conclude that negative evolution is not required at these luminosities out to z~1. (truncated)Comment: accepted for publication in ApJ Letters, 6 pages, 2 figures, uses emulateapj.st

Equilibrium distributions in thermodynamical traffic gas

We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution (for a=1) is successfully compared with the highway-traffic clearance distributions, which provides a detailed view of changes in microscopical structure of traffic sample depending on traffic density. In addition to that, the observed correspondence is a strong support of studies applying the equilibrium statistical physics to traffic modelling.Comment: 5 pages, 6 figures, changed content, added reference

The WARPS survey - IV: The X-ray luminosity-temperature relation of high redshift galaxy clusters

We present a measurement of the cluster X-ray luminosity-temperature relation out to high redshift (z~0.8). Combined ROSAT PSPC spectra of 91 galaxy clusters detected in the Wide Angle ROSAT Pointed Survey (WARPS) are simultaneously fit in redshift and luminosity bins. The resulting temperature and luminosity measurements of these bins, which occupy a region of the high redshift L-T relation not previously sampled, are compared to existing measurements at low redshift in order to constrain the evolution of the L-T relation. We find a best fit to low redshift (z1 keV, to be L proportional to T^(3.15\pm0.06). Our data are consistent with no evolution in the normalisation of the L-T relation up to z~0.8. Combining our results with ASCA measurements taken from the literature, we find eta=0.19\pm0.38 (for Omega_0=1, with 1 sigma errors) where L_Bol is proportional to (1 + z)^eta T^3.15, or eta=0.60\pm0.38 for Omega_0=0.3. This lack of evolution is considered in terms of the entropy-driven evolution of clusters. Further implications for cosmological constraints are also discussed.Comment: 11 pages, 7 figures, accepted for publication in MNRA

The Interaction of Quantum Gravity with Matter

The interaction of (linearized) gravitation with matter is studied in the causal approach up to the second order of perturbation theory. We consider the generic case and prove that gravitation is universal in the sense that the existence of the interaction with gravitation does not put new constraints on the Lagrangian for lower spin fields. We use the formalism of quantum off-shell fields which makes our computation more straightforward and simpler.Comment: 25 page

On the regularization ambiguities in loop quantum gravity

One of the main achievements of LQG is the consistent quantization of the Wheeler-DeWitt equation which is free of UV problems. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities there is the one associated to the SU(2) unitary rep. used in the diffeomorphism covariant pointsplitting regularization of nonlinear funct. of the connection. This ambiguity is labelled by a halfinteger m and, here, it is referred to as the m-ambiguity. The aim of this paper is to investigate the important implications of this ambiguity./ We first study 2+1 gravity quantized in canonical LQG. Only when the regularization of the quantum constraints is performed in terms of the fundamental rep. of the gauge group one obtains the usual TQFT. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear cut choice in the quantization of the constraints in 2+1 LQG./ We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher unit. rep. quantizations of the Hamiltonian constraint. Although the analysis is not complete in D=3+1--due to the difficulties associated to the definition of the physical inner product--it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find physical solutions associated to spin-two local excitations.Comment: 21 page

The WARPS Survey. VIII. Evolution of the Galaxy Cluster X-ray Luminosity Function

We present measurements of the galaxy cluster X-ray Luminosity Function (XLF) from the Wide Angle ROSAT Pointed Survey (WARPS) and quantify its evolution. WARPS is a serendipitous survey of the central region of ROSAT pointed observations and was carried out in two phases (WARPS-I and WARPS-II). The results here are based on a final sample of 124 clusters, complete above a flux limit of 6.5 10E-15 erg/s/cm2, with members out to redshift z ~ 1.05, and a sky coverage of 70.9 deg2. We find significant evidence for negative evolution of the XLF, which complements the majority of X-ray cluster surveys. To quantify the suggested evolution, we perform a maximum likelihood analysis and conclude that the evolution is driven by a decreasing number density of high luminosity clusters with redshift, while the bulk of the cluster population remains nearly unchanged out to redshift z ~ 1.1, as expected in a low density Universe. The results are found to be insensitive to a variety of sources of systematic uncertainty that affect the measurement of the XLF and determination of the survey selection function. We perform a Bayesian analysis of the XLF to fully account for uncertainties in the local XLF on the measured evolution, and find that the detected evolution remains significant at the 95% level. We observe a significant excess of clusters in the WARPS at 0.1 < z < 0.3 and LX ~ 2 10E42 erg/s compared with the reference low-redshift XLF, or our Bayesian fit to the WARPS data. We find that the excess cannot be explained by sample variance, or Eddington bias, and is unlikely to be due to problems with the survey selection function.Comment: 13 pages, 12 figures, accepted for publication in MNRA