Geometric Modular Action, Wedge Duality and Lorentz Covariance are Equivalent for Generalized Free Fields

The Tomita-Takesaki modular groups and conjugations for the observable algebras of space-like wedges and the vacuum state are computed for translationally covariant, but possibly not Lorentz covariant, generalized free quantum fields in arbitrary space-time dimension d. It is shown that for $d\geq 4$ the condition of geometric modular action (CGMA) of Buchholz, Dreyer, Florig and Summers \cite{BDFS}, Lorentz covariance and wedge duality are all equivalent in these models. The same holds for d=3 if there is a mass gap. For massless fields in d=3, and for d=2 and arbitrary mass, CGMA does not imply Lorentz covariance of the field itself, but only of the maximal local net generated by the field

Group Cohomology, Modular Theory and Space-time Symmetries

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for the existence of a covariant action of the (universal covering of) the Poincar\'e group. In particular this gives, together with our previous results, an intrinsic characterization of positive-energy conformal pre-cosheaves of von Neumann algebras. To this end we adapt to our use Moore theory of central extensions of locally compact groups by polish groups, selecting and making an analysis of a wider class of extensions with natural measurable properties and showing henceforth that the universal covering of the Poincar\'e group has only trivial central extensions (vanishing of the first and second order cohomology) within our class.Comment: 18 pages, plain TeX, preprint Roma Tor vergata n. 20 dec. 9

Non Symmetric Dirichlet Forms on Semifinite von Neumann Algebras

The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied.Comment: 32 pages, plain TeX, Preprint Roma TOR VERGATA Nr.9-93-May 9

Modular localization and Wigner particles

We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincare' group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh-Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and de Sitter spacetime.Comment: 22 pages, LaTeX. Some errors have been corrected. To appear on Rev. Math. Phy

An Improved Splitting Function for Small x Evolution

We summarize our recent result for a splitting function for small x evolution which includes resummed small x logarithms deduced from the leading order BFKL equation with the inclusion of running coupling effects. We compare this improved splitting function with alternative approaches.Comment: 5 pages, 2 figures, presented by G.A.at DIS200

Singlet parton evolution at small x: a theoretical update

This is an extended and pedagogically oriented version of our recent work, in which we proposed an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach.Comment: 30 pages, 8 figures, latex with sprocl.sty and epsfi

Sources of Identifying Information in Evaluation Models

The average effect of social programs on outcomes such as earnings is a parameter of primary interest in econometric evaluations studies. New results on using exclusion restrictions to identify and estimate average treatment effects are presented. Identification is achieved given a minimum of parametric assumptions, initially without reference to a latent index framework. Most econometric analyses of evaluation models motivate identifying assumptions using models of individual behavior. Our technical conditions do not fit easily into a conventional discrete choice framework, rather they fit into a framework where the source of identifying information is institutional knowledge regarding program administration. This framework also suggests an attractive experimental design for research using human subjects, in which eligible participants need not be denied treatment. We present a simple instrumental variables estimator for the average effect of treatment on program participants, and show that the estimator attains Chamberlain's semi-parametric efficiency bound. The bias of estimators that satisfy only exclusion restrictions is also considered.