论文标题
预先测定方法中新的一般相对性的主要约束分类
Classification of primary constraints for new general relativity in the premetric approach
论文作者
论文摘要
我们介绍了一种新的程序，以研究基于预先测定方法定义的本构张量中编码的数学特性的新一般相对性（NGR）的形式。我们将典型的动量共轭得出到四局场，并研究Hessian Tensor的特征值，Hessian张量的特征值借助索引公式映射到Hessian基质。 Hessian矩阵的属性在很大程度上依赖于免费系数的可能值$ c_i，i = 1,2,3 $出现在NGR Lagrangian中。我们发现在动量的时间部分中与小主要约束相关的四个无效特征值。其余的特征值分组为四组，具有多重性3、1、5和3，可以将其设置为零，具体取决于系数的不同选择$ C_I $。当一组，二或三组特征值同时消失时，有九种可能的情况有九种不同的情况。所有情况都会导致不同数量的主要约束，这与Blixt等人对NGR的先前工作一致。 （2018）。
We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients $c_i, i=1,2,3$ appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients $c_i$. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).
