Poincar\'e Supersymmetry Representations Over Trace Class Noncommutative Graded Operator Algebras

We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges, constructed from fields that form a trace class noncommutative graded operator algebra. In particular, supersymmetry theories can be turned into supersymmetric matrix models this way. We demonstrate our results by detailed component field calculations for the Wess-Zumino and the supersymmetric Yang-Mills models (the latter with axial gauge fixing), and then show that they are also implied by a simple and general superspace argument.Comment: plaintex, 23 Page

Short Distance Behavior of (2+1)-dimensional QCD

Within the framework of semiclassical QCD approximations the short distance behavior of two static color charges in (2+1)-dimensional QCD is discussed. A classical linearization of the field equations is exhibited and leads to analytical results producing the static potential. Beyond the dominant classical part proportional to ln lambda R, QCD contributions of order R^1/2 and R are found.Comment: 9 pages, uses LaTeX and elsart.st

A Strategy for a Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking

Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace action becomes the statement $0=Re Tr T_{\mu}^{\mu}$, with $T_{\mu \nu}$ the operator stress energy tensor, and with $Tr$ the trace over the underlying Hilbert space. We show that this condition implies the vanishing of the cosmological constant and vacuum energy in the emergent quantum field theory. However, since the scale invariance condition does not require the operator $T_{\mu}^{\mu}$ to vanish, the spontaneous breakdown of scale invariance is still permitted.Comment: Second award in the Gravity Research Foundation Essay Competition for 1997; to appear in General Relativity and Gravitation. Plain Tex, no figure

Nowhere dense graph classes, stability, and the independence property

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of cliques that occur as (topological) r-minors. We observe that this tameness notion from algorithmic graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence property.Comment: 9 page

Probing High Parton Densities at Low-xx in d+Au Collisions at PHENIX Using the New Forward and Backward Muon Piston Calorimeters

The new forward Muon Piston Calorimeters allow PHENIX to explore low-$x$ parton distributions in d+Au collisions with hopes of observing gluon saturation. We present a two-particle azimuthal $\Delta \phi$ correlation measurement made between a mid-rapidity particle ($|\eta_1| < 0.35$) and a forward $\pi^0$ ($3.1 < \eta_2 < 3.9$) wherein we compare correlation widths in d+Au to p+p and compute $I_{dA}$.Comment: 4 pages, 3 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

Generalized Quantum Dynamics as Pre-Quantum Mechanics

We address the issue of when generalized quantum dynamics, which is a classical symplectic dynamics for noncommuting operator phase space variables based on a graded total trace Hamiltonian ${\bf H}$, reduces to Heisenberg picture complex quantum mechanics. We begin by showing that when ${\bf H}={\bf Tr} H$, with $H$ a Weyl ordered operator Hamiltonian, then the generalized quantum dynamics operator equations of motion agree with those obtained from $H$ in the Heisenberg picture by using canonical commutation relations. The remainder of the paper is devoted to a study of how an effective canonical algebra can arise, without this condition simply being imposed by fiat on the operator initial values. We first show that for any total trace Hamiltonian which involves no noncommutative constants, there is a conserved anti--self--adjoint operator $\tilde C$ with a structure which is closely related to the canonical commutator algebra. We study the canonical transformations of generalized quantum dynamics, and show that $\tilde C$ is a canonical invariant, as is the operator phase space volume element. The latter result is a generalization of Liouville's theorem, and permits the application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values. We give arguments based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics, suggesting that statistical ensemble averages of Weyl ordered polynomials in the operator phase space variables correspond to the Wightman functions of a unitary complex quantum mechanics, with a conserved operator Hamiltonian and with the standard canonical commutation relations obeyed by Weyl ordered operator strings. Thus there is a well--defined sense inComment: 79 pages, no figures, plain te

Latest Results on the Hot-Dense Partonic Matter at RHIC

At the Relativistic Heavy Ion Collider (RHIC) collisions of heavy ions at nucleon-nucleon energies of 200 GeV appear to have created a new form of matter thought to be a deconfined state of the partons that ordinarily are bound in nucleons.We discuss the evidence that a thermalized partonic medium, usually called a Quark Gluon Plasma (QGP), has been produced. Then we discuss the effect of this high-density medium on the production of jets and their pair correlations. Next we look at direct photons as a clean electro-magnetic probe to constrain the initial hard scatterings. Finally we review the developing picture for the effect of this medium on the production of open heavy quarks and on the screening by the QGP of heavy-quark bound states.Comment: 6 pages, 14 figures, proceedings for QNP06 (5-10 June, 2006) invited tal

Results on High p_T Particle Production from the PHENIX Experiment at RHIC

Transverse momentum (p_T) spectra of neutral pions and charged hadrons measured in Au+Au and d+Au collisions at sqrt{s_NN}=200 GeV by the PHENIX experiment at RHIC are compared to p+p reference spectra at the same sqrt{s_NN}. In central Au+Au collisions a factor 4-5 suppression for neutral pions and charged hadrons with p_T > 5 GeV/c is found relative to the p+p reference scaled by the nuclear overlap function . In contrast, such a suppression of high p_T particles is absent in d+Au collisions.Comment: To appear in the proceedings of the 8th International Conference on Nucleus-Nucleus Collisions (NN 2003), Moscow, Russia, 17-21 Jun 2003 (4 pages, 3 figures), V1: error fixed in caption of Fig.

Structure of Fluctuation Terms in the Trace Dynamics Ward Identity

We give a detailed analysis of the anti-self-adjoint operator contribution to the fluctuation terms in the trace dynamics Ward identity. This clarifies the origin of the apparent inconsistency between two forms of this identity discussed in Chapter 6 of our recent book on emergent quantum theory.Comment: TeX; 14 pages. Dedicated to Rafael Sorkin on the occasion of his 60th birthda

Nonlinear PDEs for gap probabilities in random matrices and KP theory

Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are intimately related to wave functions for polynomial (Gel'fand-Dickey reductions) or rational reductions of the KP-hierarchy; their Fredholm determinant also satisfies linear PDEs (Virasoro constraints), yielding, in a systematic way, non-linear PDEs for the Fredholm determinant of such kernels. Examples include Fredholm determinants giving the gap probability of some infinite-dimensional diffusions, like the Airy process, with or without outliers, and the Pearcey process, with or without inliers.Comment: Minor revision: accepted for publication on Physica