论文标题
哈密顿量和差异性约束概括用于时机和间距3+1叶叶
Hamiltonian and Diffeomorphism Constraints Generalized for Timelike and Spacelike 3+1 Foliation
论文作者
论文摘要
sen-ashtekar-barbero-immmirzi变量中的汉密尔顿和差异性约束的形式是众所周知的3+1 ADM叶。还知道，Sen-Ashtekar-Barbero-immirzi连接只能在3维空间中引入，并且不适用于$ d> 3 $。它在$ d = 3 $中起作用的原因是由于$（3）$代数和$ r^3 $ space的同构存在。事实证明，相对于其向量产品，$（2,1）$代数和$ r^3_ {2,1} $ space代数之间存在类似的同构。通过使用这种同构，我们发现sen-ashtekar-barbero-immirzi连接的类似物用于及时的3+1叶叶，也是高斯的相应形式，差异性和哈密顿的约束。然后，我们将空间类和时型叶面约束结合到哈密顿量的广义形式，并使用广义的sen-ashtekar-barbero-immirzi连接变量约束。我们证明，Immirzi参数在时间型间距类叶叶上的变化方面是协变量的，就像在自偶联的Ashtekar案例中，它在Hamiltionian约束中消失了。
The form of Hamiltonian and Diffeomorphism constraints in Sen-Ashtekar-Barbero-Immirzi variables is well known for the spacelike 3+1 ADM foliation. It is also known that Sen-Ashtekar-Barbero-Immirzi connection can be introduced only in 3 dimensional space and does not work for $D > 3$. The reason it works in $D = 3$ is due to existence of isomorphism between $so(3)$ algebra and $R^3$ space with vector product. It turns out that similar isomorphism exists between $so(2,1)$ algebra and $R^3_{2,1}$ space algebra with respect to its vector product. By using this isomorphism we find both analog of Sen-Ashtekar-Barbero-Immirzi connection for timelike 3+1 foliation and corresponding forms of Gauss, Diffeomorphism and Hamiltonian constraints. We then combine spacelike and timelike foliation constraints into the generalized form of the Hamiltonian and Diffeomorphism constrains using generalized Sen-Ashtekar-Barbero-Immirzi connection variables. We prove that Immirzi parameter is covariant with respect to timelike-spacelike ADM foliation change as in both cases in self-dual Ashtekar case it disappears in Hamiltionian constraint keeping it polynomial.
