New methods in conformal partial wave analysis

We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.Comment: 16 page

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

ANTIBODIES DIRECTED TO INDIVIDUAL HISTONES IN JUVENILE CHRONIC ARTHRITIS. ASSOCIATION WITH UVEITIS

The trials for identification of the specific target antigen for antinuclear antibodies (ANA) in juvenile chronic arthritis (JCA) revealed that a significant number of patients produce antibodies directed to individual histories and histone peptides. Fifty JCA patients, 58 healthy children and 58 children with autoimmune and rheumatologic disorders were studied for a presence of IgG- and IgM-antibodies against histone 1, histone 2 and histone 3 measured by ELISA. The levels of IgGand IgM-antibodies directed to histone 1, 2 and 3 were elevated in JCA as compared to the healthy controls. IgG-antibodies to histone 2 and IgM-antibodies to histone 3 also were elevated in comparison with the disease controls. IgG- and IgM-antibodies against histone 1 were found to be positive in 30 % and 26 % of JCA patients, respectively, in significant association with ANA (p = 0,038 and p = 0,03, respectively) and uveitis (p = 0,02 and p = 0,016, respectively). The same prevalence of IgG- and IgM-antibodies to histone 2 was established but only the IgG-isotype showed significant association with uveitis (p = 0,018). Anti-histone 3 IgG- and IgM-antibodies were found in 34 % and 27 % of JCA patients, respectively. IgM-antibodies to histone 3 were proved to be significantly associated with uveitis (p - 0,009). It was concluded that antibodies to histone 1, histone 2, and histone 3 represented a common serological feature of JCA. Their presence was related to the manifestation of chronic anterior uveitis, associated with JCA

One-Loop Determinant of Dirac Operator in Non-Renormalizable Models

We use proper-time regularizations to define the one-loop fermion determinant in the form suggested by Gasser and Leutwyler some years ago. We show how to obtain the polynomial by which this definition of ln det D needs to be modified in order to arrive at the fermion determinant whose modulus is invarinat under chiral transformations. As an example it is shown how the fundamental symmetries associated with the NJL model are preserved in a consistent way.Comment: 8 pages, LaTe

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