Noncommutative Differential Calculus and Its Application on Discrete Spaces

• 来源期刊: 理论物理通讯(英文版)
• 年，卷（期）: 2008,（1）
• 页码范围: 37-44
• 页数: 8页
• 语种: 英文

摘要

We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincar(e) lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.