Hamilton Dynamics on Clifford Kaehler Manifolds

Mechanics Systems on Para-Kaehlerian Manifolds of Constant J-Sectional Curvature

The goal of this paper is to present Euler-Lagrange and Hamiltonian equations on R2n which is a model of para-Kaehlerian manifolds of constant J-sectional curvature. In conclusion, some differential geometrical and physical results on the related mechanic systems have been given.

Bi-orthogonal eigen-spinors related to T-pseudo-Hermitian Pauli Hamiltonian : Time reversal and Clifford Algebra

A set of two-parameter bi-orthogonal eigen-spinors has been constructed from a deformed pseudo- Hermitian extension of Pauli Hamiltonian and its Hermitian conjugate. The Hamiltonians thus obtained are iso-spectral to the original Pauli Hamiltonian. A pair of spin-projection operators has been constructed as an essential ingredient of a possible bi-orthogonal quantum mechanics. An analogue of Kramers theorem in pseudo-Hermitian setting has also been inferred in a conjectural sense. The properties of time reversal and bi-orthogonality have been elaborated in the frame work of Clifford algebra Cl…

克莱因代数上的相空间结构

Phase Space structure on Clifford Algebras

本文通过霍奇结构将凯勒结构推广到更高维度，为克莱因代数赋予相空间结构，从而在多重线性变量上构建哈密顿动力学。

The Relativistic Hamilton-Jacobi Equation for a Massive, Charged and Spinning Particle, its Equivalent Dirac Equation and the de Broglie-Bohm Theory

Using the Clifford and the Spin-Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle interacting with an external electromagnetic field is equivalent to a Dirac-Hestenes equation satisfied by a class of spinor fields that we call classical spinor fields, characterized for having the Takabayashi angle function constant (equal to 0 or π). We also investigate a nonlinear Dirac-Hestenes like equation that comes from some class of generalized classical spinor fields. Finally we show that the general Dirac-Hestenes equati…

Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity

The book contains a collection of works on Riemann-Cartan and metric-affine manifolds provided with nonlinear connection structure and on generalized Finsler-Lagrange and Cartan-Hamilton geometries and Clifford structures modelled on such manifolds. The choice of material presented has evolved from various applications in modern gravity and geometric mechanics and certain generalizations to noncommutative Riemann-Finsler geometry. The authors develop and use the method of anholonomic frames with associated nonlinear connection structure and apply it to a number of concrete problems: constructi…

幺正动力学的拓扑相：Clifford范畴中的分类

Topological phases of unitary dynamics: Classification in Clifford category

本文研究幺正动力学的拓扑相分类问题，针对Clifford范畴中平移不变的Clifford QCA，通过维数下降方法得到任意空间维度下模Clifford量子电路和移位的完整群分类表。