Baby and I

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Towards a Nonperturbative Path Integral in Gauge Theories

We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is based on the Kato-Trotter product formula modified appropriately to incorporate the gauge invariance condition, and thereby equivalence to the Dirac operator formalism is guaranteed by construction. The modified path integral provides a solution to the Gribov obstruction as well as to the operator ordering problem when the orbit space has curvature. A few explicit examples are given to illustrate new features of the formalism developed. The method is applied to the Kogut-Susskind lattice gauge theory to develop a nonperturbative functional integral for a quantum Yang-Mills theory. Feynman's conjecture about a relation between the mass gap and the orbit space geometry in gluodynamics is discussed in the framework of the modified path integral.Comment: plain Latex, 12 pages, a few changes made and some comments added, a final version to appear in Phys. Lett.

Coordinate-Free Quantization of Second-Class Constraints

The conversion of second-class constraints into first-class constraints is used to extend the coordinate-free path integral quantization, achieved by a flat-space Brownian motion regularization of the coherent-state path integral measure, to systems with second-class constraints.Comment: 21 pages, plain LaTeX, no figure

The Connection Between Diffuse Light and Intracluster Planetary Nebulae in the Virgo Cluster

We compare the distribution of diffuse intracluster light detected in the Virgo Cluster via broadband imaging with that inferred from searches for intracluster planetary nebulae (IPNe). We find a rough correspondence on large scales (~ 100 kpc) between the two, but with very large scatter (~ 1.3 mag/arcsec^2). On smaller scales (1 -- 10 kpc), the presence or absence of correlation is clearly dependent on the underlying surface brightness. On these scales, we find a correlation in regions of higher surface brightness (mu_V < ~27) which are dominated by the halos of large galaxies such as M87, M86, and M84. In those cases, we are likely tracing PNe associated with galaxies rather than true IPNe. In true intracluster fields, at lower surface brightness, the correlation between luminosity and IPN candidates is much weaker. While a correlation between broadband light and IPNe is expected based on stellar populations, a variety of statistical, physical, and methodological effects can act to wash out this correlation and explain the lack of a strong correlation at lower surface brightness found here. [abridged

Wave Propagation in Stochastic Spacetimes: Localization, Amplification and Particle Creation

Here we study novel effects associated with electromagnetic wave propagation in a Robertson-Walker universe and the Schwarzschild spacetime with a small amount of metric stochasticity. We find that localization of electromagnetic waves occurs in a Robertson-Walker universe with time-independent metric stochasticity, while time-dependent metric stochasticity induces exponential instability in the particle production rate. For the Schwarzschild metric, time-independent randomness can decrease the total luminosity of Hawking radiation due to multiple scattering of waves outside the black hole and gives rise to event horizon fluctuations and thus fluctuations in the Hawking temperature.Comment: 26 pages, 1 Postscript figure, submitted to Phys. Rev. D on July 29, 199

Energy, Aesthetics and Knowledge in Complex Economic Systems

It is argued that the fact that economic systems are dissipative structures must be taken fully into account in economics if we are to understand the nature of the economic-ecological interface and how to deal with emergent environmental problems, such as global warming. Such problems are a product of economic growth, which is widely accepted to be the outcome of the acquisition and application of knowledge. Drawing upon disparate literatures within and outside economics, it is argued that economic growth should be more properly viewed as the outcome of a co-evolutionary process that involves the autocatalytic interaction of new knowledge and access of increasing amounts of free energy to do increasingly specialized forms of work. The conventional view is that energy is just a factor of production used increasingly as new knowledge is employed. The possibility of reverse causation is considered here. Specifically, the relevance of the ‘energy hypothesis,’ associated with Eric Schneider and his collaborators, is assessed. This hypothesis states that all dissipative structures have, as their primary objective, the reduction of accessible free energy gradients. It is concluded that such a hypothesis cannot be rejected in the context of economic behaviour and that this opens up an important research agenda for economists. It is argued that such research has to be interdisciplinary because our economic behaviour is driven by aspirational goals which are aesthetic constructions in the mind and strongly connected to our emotions. In this regard, recent neuropsychological literature, arguing that certain emotional dispositions are necessary before we can employ our cognitive capabilities effectively, is important to digest. Thus, the possibility exists that it is in the emotional domain of the mind that the energy hypothesis is operative. Aesthetic constructions are, thus, connecting agents in the knowledge-energy co-evolutionary process. Some of the macroeconomic evidence concerning the relationship between free energy use and economic growth is considered and it is found that the energy hypothesis cannot be rejected in the economic domain. However, considerably more research needs to be undertaken before any firm conclusions can be drawn

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at sNN=200\sqrt{s_{NN}} = 200 GeV

Identified mid-rapidity particle spectra of $\pi^{\pm}$, $K^{\pm}$, and $p(\bar{p})$ from 200 GeV p+p and d+Au collisions are reported. A time-of-flight detector based on multi-gap resistive plate chamber technology is used for particle identification. The particle-species dependence of the Cronin effect is observed to be significantly smaller than that at lower energies. The ratio of the nuclear modification factor ($R_{dAu}$) between protons $(p+\bar{p})$ and charged hadrons ($h$) in the transverse momentum range $1.2<{p_{T}}<3.0$ GeV/c is measured to be $1.19\pm0.05$(stat)$\pm0.03$(syst) in minimum-bias collisions and shows little centrality dependence. The yield ratio of $(p+\bar{p})/h$ in minimum-bias d+Au collisions is found to be a factor of 2 lower than that in Au+Au collisions, indicating that the Cronin effect alone is not enough to account for the relative baryon enhancement observed in heavy ion collisions at RHIC.Comment: 6 pages, 4 figures, 1 table. We extended the pion spectra from transverse momentum 1.8 GeV/c to 3. GeV/

Azimuthal anisotropy at RHIC: the first and fourth harmonics

We report the first observations of the first harmonic (directed flow, v_1), and the fourth harmonic (v_4), in the azimuthal distribution of particles with respect to the reaction plane in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). Both measurements were done taking advantage of the large elliptic flow (v_2) generated at RHIC. From the correlation of v_2 with v_1 it is determined that v_2 is positive, or {\it in-plane}. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 6 pages with 3 figures, as accepted for Phys. Rev. Letters The data tables are at http://www.star.bnl.gov/central/publications/pubDetail.php?id=3

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)