N-bein，Einstein-Cartan，引力在任意维中的哈密顿公式：进展报告（CAIMS-2009演讲的扩展版，6月11-14日，伦敦，加拿大）
The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity in any dimension: the Progress Report (Extended version of a talk given on CAIMS-2009, June 11-14, London, Canada)
摘要：
本文分析了N-bein、Einstein-Cartan、引力的哈密顿形式，在任何大于2的维数上，都采用一阶形式。这个哈密顿公式允许明确地显示三维情况下的特殊性（\textit{A.M.Frolov et al, 0902.0856 [gr-qc]}）发生并根据本报告中的结果推测，存在一个一般的N-bein重力公式的\textit{all}维度特征：在消除第二类约束之后，剩余的第一类次级约束中的Poisson括号的代数是Poincare代数，并且在所有维度N中，bein，Cartan-Einstein，重力\textit{is the Poincare gauge theory}。对应于第一类约束代数的规范对称性有两个参数--旋转（洛伦兹）和平移。平移不变性对所有维度都是共同的，但在N-beins和连接的规范变换的一般表达式中，某些项在特定的三维情况下为零。我们的猜想的证明是详细概述。一些简单但繁琐的计算仍有待完成，以调用我们的猜想-定理，并将报告后。
英文摘要：
The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity, using its first order form in any dimension higher than two, is analyzed. This Hamiltonian formulation allows to explicitly show where peculiarities of three dimensional case (\textit{A.M.Frolov et al, 0902.0856 [gr-qc]}) occur and make a conjecture, based on presented in this report results, that there is one general for \textit{all} dimensions characteristic of N-bein formulation of gravity: after elimination of second class constraints the algebra of Poisson brackets among remaining first class secondary constraints is the Poincare algebra and in all dimensions N-bein, Cartan-Einstein, gravity \textit{is the Poincare gauge theory}. The gauge symmetry corresponding to the algebra of first class constraints has two parameters - rotational (Lorentz) and translational. Translational invariance is common to all dimensions but some terms in general expressions for gauge transformations of N-beins and connections are zero in a particular, three dimensional, case. The proof of our conjecture is outlined in detail. Some straightforward but tedious calculations remain to be completed to call our conjecture - a theorem and will be reported later.
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