A new diagrammatic representation for correlation functions in the in-in formalism

In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the equation of motion for the quantum operators with only retarded propagators, which makes each diagram intrinsically local (whereas in the standard case locality is the result of several cancellations) and endowed with a straightforward physical interpretation. While the final result is strictly equivalent, as a bonus the formulation presented here also contains less graphs than other diagrammatic approaches to in-in correlation functions. Our method is particularly suitable for applications to cosmology.Comment: 14 pages, matches the published version. includes a modified version of axodraw.sty that works with the Revtex4 clas

Holographic Construction of Excited CFT States

We present a systematic construction of bulk solutions that are dual to CFT excited states. The bulk solution is constructed perturbatively in bulk fields. The linearised solution is universal and depends only on the conformal dimension of the primary operator that is associated with the state via the operator-state correspondence, while higher order terms depend on detailed properties of the operator, such as its OPE with itself and generally involve many bulk fields. We illustrate the discussion with the holographic construction of the universal part of the solution for states of two dimensional CFTs, either on $R \times S^1$ or on $R^{1,1}$. We compute the 1-point function both in the CFT and in the bulk, finding exact agreement. We comment on the relation with other reconstruction approaches.Comment: 26 pages, 4 figures, v2: comments adde

Parallel algorithm with spectral convergence for nonlinear integro-differential equations

We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a linearized version of the problem and a spectral method where unknown functions are expanded in terms of Chebyshev polynomials (El-gendi's method). This approach is shown to be suitable for the calculation of two-point Green functions required in next to leading order studies of time-dependent quantum field theory.Comment: 15 pages, 9 figure

Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate

Time evolution of the chiral phase transition during a spherical expansion

We examine the non-equilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$ expansion. Starting at a temperature above the phase transition, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle \sigma \rangle$, and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the ``out'' regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps

Problems of Perturbation Series in Non-Equilibrium Quantum Field Theories

In the standard framework of non-equilibrium quantum field theories, the pinch singularities associated to multiple products of $\delta$-functions do not cancel in a perturbative expansion unless the particle distributions are those for a system in thermal and chemical equilibrium.Comment: 10 pages, 2 figures, Cern preprint CERN-TH.7271/9

Nonrandomized comparison of local urokinase thrombolysis versus systemic heparin anticoagulation for superior sagittal sinus thrombosis

Background and Purpose We sought to compare the safety and efficacy of direct urokinase thrombolysis with systemic heparin anticoagulation for superior sagittal sinus thrombosis (SSST). Methods At University at Buffalo (NY) and University of Texas (Dallas, Houston), we reviewed 40 consecutive patients with SSST, treated with local urokinase (thrombolysis group) or systemic heparin anticoagulation (heparin group). The thrombolysis group (n=20) received local urokinase into the SSS followed by systemic heparin anticoagulation. The heparin group (n=20) received systemic heparin anticoagulation only. Neurological dysfunction was rated as follows: 0, normal; 1, mild (but able to ambulate and communicate); 2, moderate (unable to ambulate, normal mentation); and 3, severe (unable to ambulate, altered mentation). Results Age (P=0.49), sex (P=0.20), baseline venous infarction (P=0.73), and predisposing illnesses (P=0.52) were similar between the thrombolysis and heparin groups. Pretreatment neurological function was worse in the thrombolysis group (normal, n=5; mild, n=8; moderate, n=4; severe, n=3) than in the heparin group (normal, n=8; mild, n=8; moderate, n=3; severe, n=1) (P=NS). Discharge neurological function was better in the thrombolysis group (normal, n=16; mild, n=3; moderate, n=1; severe, n=0) than in the heparin group (normal, n=9; mild, n=6; moderate, n=5; severe, n=0) (P=0.019, Mann-Whitney U test). Hemorrhagic complications were 10% (n=2) in the thrombolysis group (subdural hematoma, retroperitoneal hemorrhage) and none in the heparin group (P=0.49). Three of the heparin group patients developed complications of the underlying disease (status epilepticus, hydrocephalus, refractory papilledema). No deaths occurred. Length of hospital stay was similar between the groups (P=0.79). Conclusions Local thrombolysis with urokinase is fairly well tolerated and may be more effective than systemic heparin anticoagulation alone in treating SSST. A randomized, prospective study comparing these 2 treatments for SSST is warranted

ANALYTICAL METHOD DEVELOPMENT AND VALIDATION OF AMLODIPINE IN HUMAN PLASMA USING LIQUID CHROMATOGRAPHY-MASS SPECTROMETRY/MASS SPECTROMETRY

Objective: The objective of the present investigation was to develop a novel, simple, and economic method for the estimation of amlodipine in positive ion mode in human plasma using amlodipine maleate d4 as an internal standard.Methods: The chromatographic separation was performed on Zorbax SB, C18, 50 mm*4.6 mm, and 3.5 mm. The mobile phase was prepared with a mixture of 5 mm ammonium acetate in 0.1% formic acid: High performance liquid chromatographic (HPLC) grade methanol:HPLC grade acetonitrile (40:30:30) that run isocratically at the flow rate of 0.700 ml/min and run time at 2.50 min.Results: The analytical method is valid for the estimation of amlodipine, in human plasma over a range of 0.100 ng/ml–9.990 ng/ml with the detection of amlodipine m/z - 409.10 (parent) and 238.00 (product), and internal standard Amlodipine Maleate d4 m/z - 413.20 (parent), and 238.00 (product) in positive ion mode. The results of carryover test, matrix effect, linearity, precision and accuracy, stabilities, dilution integrity, and run size evaluation test presented in this report are within the acceptance range.Conclusion: A sensitive method for the separation and determination of amlodipine in plasma has been developed based on solid-phase extraction with disposable extraction cartridges in combination with LC and mass spectrophotometers (MS/MS)

Resumming the large-N approximation for time evolving quantum systems

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is $L(x,\dot{x}) = (1/2) \sum_{i=1}^{N} \dot{x}_i^2 - (g/8N) [ \sum_{i=1}^{N} x_i^2 - r_0^2 ]^{2}$. The key to these approximations is to treat both the $x$ propagator and the $x^2$ propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the $x^2$ propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact $x^2$ propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest $N$ better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are separately liste