Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT

Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields (see Commun. Math. Phys. 218 (2001) 417-436; hep-th/0009004). The conformal Hamiltonian $H$ has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space can be represented as finite linear combinations of basic (doubly periodic) elliptic functions in the conformal time variables (of periods 1 and $\tau$) whose coefficients are, in general, formal power series in $q^{1/2}=e^{i\pi\tau}$ involving spherical functions of the "space-like" fields' arguments. As a corollary, if the resulting expansions converge to meromorphic functions, then the finite temperature correlation functions are elliptic. Thermal 2-point functions of free fields are computed and shown to display these features. We also study modular transformation properties of Gibbs energy mean values with respect to the (complex) inverse temperature $\tau$ ($Im(\tau)=\beta/(2\pi)>0$). The results are used to obtain the thermodynamic limit of thermal energy densities and correlation functions.Comment: LaTex. 56 pages. The concept of global conformal invariance set in a historical perspective (new Sect. 1.1 in the Introduction), references added; minor corrections in the rest of the pape

H\"older-continuous rough paths by Fourier normal ordering

We construct in this article an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in(0,1)$. The method may be coined as 'Fourier normal ordering', since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. In doing so, there appear non-trivial tree combinatorics, which are best understood by using the structure of the Hopf algebra of decorated rooted trees (in connection with the Chen or multiplicative property) and of the Hopf shuffle algebra (in connection with the shuffle or geometric property). H\"older continuity is proved by using Besov norms. The method is well-suited in particular in view of applications to probability theory (see the companion article \cite{Unt09} for the construction of a rough path over multidimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or \cite{Unt09ter} for a short survey in that case).Comment: 50 pages, 6 figure

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added

Linac Coherent Light Source Undulator RF BPM System

The Linac Coherent Light Source (LCLS) will be the world's first x-ray free-electron laser (FEL) when it becomes operational in 2009. The LCLS is currently in the construction phase. The beam position monitor (BPM) system planned for the LCLS undulator will incorporate a high-resolution X-band cavity BPM system described in this paper. The BPM system will provide high-resolution measurements of the electron beam trajectory on a pulse-to-pulse basis and over many shots. The X-band cavity BPM size, simple fabrication, and high resolution make it an ideal choice for LCLS beam position detection. We will discuss the system specifications, design, and prototype test results

Design and Performance of the LCLS Cavity BPM System

In this paper we present the design of the beam position monitor (BPM) system for the LCLS undulator, which features a high-resolution X-band cavity BPM. Each BPM has a TM{sub 010} monopole reference cavity and a TM{sub 110} dipole cavity designed to operate at a center frequency of 11.384 GHz. The signal processing electronics features a low noise single-stage three-channel heterodyne receiver that has selectable gain and a phase locking local oscillator. We will discuss the system specifications, design, and prototype test results

Antibodies against CD20 or B-Cell Receptor Induce Similar Transcription Patterns in Human Lymphoma Cell Lines

BACKGROUND: CD20 is a cell surface protein exclusively expressed on B cells. It is a clinically validated target for Non-Hodgkin's lymphomas (NHL) and autoimmune diseases. The B cell receptor (BCR) plays an important role for development and proliferation of pre-B and B cells. Physical interaction of CD20 with BCR and components of the BCR signaling cascade has been reported but the consequences are not fully understood. METHODOLOGY: In this study we employed antibodies against CD20 and against the BCR to trigger the respective signaling. These antibodies induced very similar expression patterns of up- and down-regulated genes in NHL cell lines indicating that CD20 may play a role in BCR signaling and vice versa. Two of the genes that were rapidly and transiently induced by both stimuli are CCL3 and CCL4. 4 hours after stimulation the concentration of these chemokines in culture medium reaches a maximum. Spleen tyrosine kinase Syk is a cytoplasmic tyrosine kinase and a key component of BCR signaling. Both siRNA mediated silencing of Syk and inhibition by selective small molecule inhibitors impaired CCL3/CCL4 protein induction after treatment with either anti-CD20 or anti-BCR antibodies. CONCLUSION: Our results suggest that treatment with anti-CD20 antibodies triggers at least partially a BCR activation-like response in NHL cell lines