Local Primitive Causality and the Common Cause Principle in Quantum Field Theory

If \{A(V)\} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V_1 and V_2 are spacelike separated spacetime regions, then the system (A(V_1),A(V_2),\phi) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A \in A(V_1), B \in A(V_2) correlated in the normal state \phi there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V_1 and V_2 and disjoint from both V_1 and V_2, a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system (A(V_1),A(V_2),\phi) with a locally normal and locally faithful state \phi and open bounded V_1 and V_2 satisfies the Weak Reichenbach's Common Cause Principle.Comment: 14 pages, Late

Quantum Probability Theory

The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in the early thirties, as well. To precisely this end, von Neumann initiated the study of what are now called von Neumann algebras and, with Murray, made a first classification of such algebras into three types. The nonrelativistic quantum theory of systems with finitely many degrees of freedom deals exclusively with type I algebras. However, for the description of further quantum systems, the other types of von Neumann algebras are indispensable. The paper reviews quantum probability theory in terms of general von Neumann algebras, stressing the similarity of the conceptual structure of classical and noncommutative probability theories and emphasizing the correspondence between the classical and quantum concepts, though also indicating the nonclassical nature of quantum probabilistic predictions. In addition, differences between the probability theories in the type I, II and III settings are explained. A brief description is given of quantum systems for which probability theory based on type I algebras is known to be insufficient. These illustrate the physical significance of the previously mentioned differences.Comment: 28 pages, LaTeX, typos removed and some minor modifications for clarity and accuracy made. This is the version to appear in Studies in the History and Philosophy of Modern Physic

Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations

We investigate the validity of the Dirac Quantization Condition (DQC) for magnetic monopoles in noncommutative space-time. We use an approach which is based on an extension of the method introduced by Wu and Yang. To study the effects of noncommutativity of space-time, we consider the gauge transformations of $U_\star(1)$ gauge fields and use the corresponding deformed Maxwell's equations. Using a perturbation expansion in the noncommutativity parameter $\theta$, we show that the DQC remains unmodified up to the first order in the expansion parameter. The result is obtained for a class of noncommutative source terms, which reduce to the Dirac delta function in the commutative limit.Comment: 18 pages. Relation to relevant literature clarified in the conclusions, 6 references adde

Examining a reduced jet-medium coupling in Pb+Pb collisions at the Large Hadron Collider

Recent data on the nuclear modification factor $R_{AA}$ of jet fragments in 2.76 ATeV Pb+Pb collisions at the Large Hadron Collider (LHC) indicate that the jet-medium coupling in a Quark-Gluon Plasma (QGP) is reduced at LHC energies and not compatible with the coupling deduced from data at the Relativistic Hadron Collider (RHIC). We estimate the reduction factor from a combined fit to the available data on $R_{AA}(\sqrt{s},p_T,b)$ and the elliptic flow $v_2(\sqrt{s},p_T,b)$ at $\sqrt{s}=0.2,2.76$ ATeV over a transverse momentum range $p_T$ 10-100 GeV and a broad impact parameter, b, range. We use a simple analytic "polytrope" model ($dE/dx=- \kappa E^{a} x^z T^{c}$) to investigate the dynamical jet-energy loss model dependence. Varying a=0-1 interpolates between weakly-coupled and strongly-coupled models of jet-energy dependence while z=0-2 covers a wide range of possible jet-path dependencies from elastic and radiative to holographic string mechanisms. Our fit to LHC data indicates an approximate 40% reduction of the coupling $\kappa$ from RHIC to LHC and excludes energy-loss models characterized by a jet-energy exponent with a>1/3. In particular, the rapid rise of $R_{AA}$ with $p_T$>10 GeV combined with the slow variation of the asymptotic $v_2(p_T)$ at the LHC rules out popular exponential geometric optics models (a=1). The LHC data are compatible with $0\leq a\leq 1/3$ pQCD-like energy-loss models where the jet-medium coupling is reduced by approximately 10% between RHIC and LHC.Comment: 10 pages, 7 figures, version published in Physical Review

Fourier Harmonics of High-pT Particles Probing the Fluctuating Intitial Condition Geometries in Heavy-Ion Collisions

Second Fourier harmonics of jet quenching have been thoroughly explored in the literature and shown to be sensitive to the underlying jet path-length dependence of energy loss and the differences between the mean eccentricity predicted by Glauber and CGC/KLN models of initial conditions. We compute the jet path-length dependence of energy-loss for higher azimuthal harmonics of jet-fragments in a generalized model of energy-loss for RHIC energies and find, however, that even the high-$p_T$ second moment is most sensitive to the poorly known early-time evolution during the first fm/c. Moreover, we demonstrate that higher-jet harmonics are remarkably insensitive to the initial conditions, while the different $v_n(N_{part})$ vs. $v_n^{I_{AA}}(N_{part})$ correlations between the moments of monojet and dijet nuclear modifications factors remain a most sensitive probe to differentiate between Glauber and CGC/KLN initial state sQGP geometries.Comment: 6 pages, 7 figures, updated figures, version accepted for publication in Phys. Rev.

Open Charm and Beauty at Ultrarelativistic Heavy Ion Colliders

Important goals of RHIC and LHC experiments with ion beams include the creation and study of new forms of matter, such as the Quark Gluon Plasma. Heavy quark production and attenuation will provide unique tomographic probes of that matter. We predict the suppression pattern of open charm and beauty in $Au+Au$ collisions at RHIC and LHC energies based on the DGLV formalism of radiative energy loss. A cancelation between effects due to the $\sqrt{s}$ energy dependence of the high $p_T$ slope and heavy quark energy loss is predicted to lead to surprising similarity of heavy quark suppression at RHIC and LHC.Comment: 4 pages, 6 *.eps files combined into 4 figure

Differential freezeout and pion interferometry at RHIC from covariant transport theory

Puzzling discrepancies between recent pion interferometry data on Au+Au reactions at s^1/2 = 130 and 200 AGeV from RHIC and predictions based on ideal hydrodynamics are analyzed in terms of covariant parton transport theory. The discrepancies of out and longitudinal radii are significantly reduced when the finite opacity of the gluon plasma is taken into account.Comment: 4 pages, 3 EPS figures. Submitted to PR

Di-Jet Conical Correlations Associated with Heavy Quark Jets in anti--de Sitter Space/Conformal Field Theory Correspondence

We show that far zone Mach and diffusion wake ``holograms'' produced by supersonic strings in anti--de Sitter space/conformal field theory (AdS/CFT) correspondence do not lead to observable conical angular correlations in the strict $N_c\to\infty$ supergravity limit if Cooper-Frye hadronization is assumed. However, a special {\em nonequilibrium} ``neck'' zone near the jet is shown to produce an apparent sonic boom azimuthal angle distribution that is roughly independent of the heavy quark's velocity. Our results indicate that a measurement of the dependence of the away-side correlations on the velocity of associated identified heavy quark jets at the BNL Relativistic Heavy Ion Collider and CERN LHC will provide a direct test of the nonperturbative dynamics involved in the coupling between jets and the strongly-coupled Quark-Gluon Plasma (sQGP) implied by AdS/CFT correspondence.Comment: 4 pages, 2 figures, version published in Physical Review Letter

Near Zone Navier-Stokes Analysis of Heavy Quark Jet Quenching in an N\mathcal{N} =4 SYM Plasma

The near zone energy-momentum tensor of a supersonic heavy quark jet moving through a strongly-coupled $\mathcal{N}=4$ SYM plasma is analyzed in terms of first-order Navier-Stokes hydrodynamics. It is shown that the hydrodynamical description of the near quark region worsens with increasing quark velocities. For realistic quark velocities, $v=0.99$, the non-hydrodynamical region is located at a narrow band surrounding the quark with a width of approximately $3/\pi T$ in the direction parallel to the quark's motion and with a length of roughly $10/\pi T$ in the perpendicular direction. Our results can be interpreted as an indication of the presence of coherent Yang-Mills fields where deviation from hydrodynamics is at its maximum. In the region where hydrodynamics does provide a good description of the system's dynamics, the flow velocity is so small that all the nonlinear terms can be dropped. Our results, which are compatible with the thermalization timescales extracted from elliptic flow measurements, suggest that if AdS/CFT provides a good description of the RHIC system, the bulk of the quenched jet energy has more than enough time to locally thermalize and become encoded in the collective flow. The resulting flow pattern close to the quark, however, is shown to be considerably different than the superposition of Mach cones and diffusion wakes observed at large distances.Comment: new revised version, 11 figures, as published in PR