论文标题
几乎换向光谱三元组和纺纱束上的量子扩散
Quantum diffusion on almost commutative spectral triples and spinor bundles
论文作者
论文摘要
Based on the observation that Cacic [10]'s characterization of almost commutative spectral triples as Clifford module bundles can be pushed to endomorphim algebras of Dirac bundles, with the geometric Dirac operator related to the Dirac operator of the spectral triple by a perturbation, the question of complete positivity of the heat semigroups generated by connection laplacian and Dirac and Kostant's cubic使用自旋几何形状和C *-Dirichlet形式来接近Dirac Laplacians。旋转捆绑包的内晶代数的几何热半元组被证明是量子动力学半群，并且使用sinha and goswami的构造建立了与还原均质空间相关的旋转半束相关的协变量量子随机流。
Based on the observation that Cacic [10]'s characterization of almost commutative spectral triples as Clifford module bundles can be pushed to endomorphim algebras of Dirac bundles, with the geometric Dirac operator related to the Dirac operator of the spectral triple by a perturbation, the question of complete positivity of the heat semigroups generated by connection laplacian and Dirac and Kostant's cubic Dirac laplacians is approached using spin geometry and C *-Dirichlet forms. The geometric heat semigroups for on endomorphosm algebras of spinor bundles are shown to be quantum dynamical semigroups and the existence of covariant quantum stochastic flows associated to the heat semigroups on spinor bundles over reductive homogeneous spaces is established using the construction of Sinha and Goswami [34].
