We shall establish the core of singular integral theory and pseudodifferential calculus over archetypal algebras noncommutative geometry: quantum forms Euclidean spaces tori. Our results go beyond Connes’ for rotation algebras, thanks to a new form Calderón-Zygmund these which crucially incorporates nonconvolution kernels. deduce <mml:math xmlns:mml="...

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical principle we give presentations of the quantum cohomology algebras. These algebras are semi-simple for adjoint non coadjoint varieties and some properties of th...

Quantum causal histories are defined to be causal sets with Hilbert spaces attached to each event and local unitary evolution operators. The reflexivity, antisymmetry, and transitivity properties of a causal set are preserved in the quantum history as conditions on the evolution operators. A quantum causal history in which transitivity holds can be treated as “directed” topological quantum fiel...