Gluing Noncommutative Twistor Spaces

A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere

The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subject to an appropriate local boundary condition. We show that the resulting operators have compact resolvents, and so they are elliptic operators.

Twistor algebraic dynamics in complex space-time and physical meaning of hidden dimensions

We review the algebraic field theory based completely on a nonlinear generalization of the CR complex analiticity conditions to the noncommutative algebra of biquaternions. Any biquaternionic field possesses natural twistor structure and, in the Minkowski space, gives rise to a shear-free null congruence of rays and to a set of gauge fields associated with it. In the paper we develop the algebrodynamical scheme in the complex extension of Minkowski space-time -- in the full vector space of biquaternion algebra. This primodial space dynamically reduces to the 6D ``observable'' space-time of the…

Penrose--Sparling非Hausdorff扭量空间的循环源配对

Cyclic source pairings for Penrose--Sparling non-Hausdorff twistor spaces

通过引入非交换几何技术，利用显式的étale粘合群胚及其卷积代数重新解释反自对偶Coulomb场的Penrose--Sparling非Hausdorff扭量空间，并计算两种Chern--Connes配对，其中源适配的循环配对恢复Coulomb荷。

Crystals, instantons and quantum toric geometry

We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological string theory and quantum gravity. Its partition function can be computed by enumerating the contributions from noncommutative instantons to a six-dimensional cohomological gauge theory, which yields a dynamical realization of the crystal as a discretization of spacetime at the Planck scale. We describe analogous relations between a melting crystal model in two d…