Schwinger Terms and Cohomology of Pseudodifferential Operators

We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the ``twisted'' Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry. In the process we also show how the ordinary Radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component.Comment: 19 pages, plain te

Spectral action for Bianchi type-IX cosmological models

In this paper we prove a rationality phenomena for the coefficients of the heat kernel expansion of the Dirac-Laplacian of Bianchi IX cosmological models. Due the complexities arising from the anisotropic nature of the model, we present a novel method of writing the heat coefficients as Wodzicki resiudes of certain Laplacians and then provide an elegant proof of the rationality result. That is, we show that each coefficient is described by a several variable polynomial with rational coefficients of the cosmic expansion factors and their higher derivatives of a certain order. This result confirms the arithmetic nature of the complicated terms in the expansion

CSCL for intellectually disabled pupils : stimulating interaction by using a floor control mechanism

Computer-supported collaborative learning has an unexploited potential of becoming an effective learning method for pupils with intellectual disabilities. This paper aims at showing how some specific requirements of this target group may be met by structuring a learning situation with the help of floor control, which restricts the opportunities of a learning dyad to act simultaneously within the learning environment. It was expected that floor control could improve communication between pupils with intellectual disabilities by explicitly structuring and restricting activities in the learning environment and making it necessary for the pupils to communicate. To examine if floor control really supports the collaboration process in the hypothesized way, two different versions of a CSCL environment were implemented and compared. The results revealed improved task-related communication and a higher quality of interaction outcomes