arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1802.02130gr-qchep-th
收藏

f（T）引力的Hamilton形式

Hamiltonian formalism for f(T) gravity

Rafael Ferraro, María José Guzmán

备注：
15 pages, no figures, comments welcome; references added; typos corrected, matches the published version
发表信息：
Phys. Rev. D 97, 104028 (2018)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

给出了$f(T)$引力的哈密顿形式，证明了该理论具有$\frac{n(n-3)}{2}+1$自由度（d.o.f.）在$n$维度上。我们开始从标量张量作用的理论，它表示一个标量场最小耦合的扭转标量$T$，定义了远程平行等效的广义相对论（TEGR）拉格朗日。$T$被写为Vierbein的非完整性系数的二次形式。通过对正则动量定义中涉及的多指标矩阵特征值结构的分析，得到了正则动量的主要约束条件。辅助标量场产生一个额外的主要约束时，与TEGR的情况相比。次级约束是超哈密顿量和超动量约束，它们是从GR的Arnowitt-Deser-Misner公式中保留下来的。有一组$\frac{n(n-1)}{2}$初级约束表示理论的局部洛伦兹变换，它们可以组合起来形成一组$\frac{n(n-1)}{2}-1$第一类约束，而其中一个成为第二类约束。由于约束之间的括号矩阵的结构，该结果与维数无关。由于这种局部洛伦兹破坏，第一类正则哈密顿量被修改，并且成为第二类的唯一一个局部洛伦兹变换与第二类约束$π\approx 0$配对以去除一个d.o.f.。从典型变量的$n^2+1$对。其余的$\frac{n(n-1)}{2}+2n-1$主约束去除相同数量的d.o.f.，只剩下$\frac{n(n-3)}{2}+1$ d.o.f.的理论。这意味着$f(T)$重力只有一个额外的自由度，其可以被解释为标量d.o.f.。

英文摘要：

We present the Hamiltonian formalism for $f(T)$ gravity, and prove that the theory has $\frac{n(n-3)}{2}+1$ degrees of freedom (d.o.f.) in $n$ dimensions. We start from a scalar-tensor action for the theory, which represents a scalar field minimally coupled with the torsion scalar $T$ that defines the teleparallel equivalent of general relativity (TEGR) Lagrangian. $T$ is written as a quadratic form of the coefficients of anholonomy of the vierbein. We obtain the primary constraints through the analysis of the structure of the eigenvalues of the multi-index matrix involved in the definition of the canonical momenta. The auxiliary scalar field generates one extra primary constraint when compared with the TEGR case. The secondary constraints are the super-Hamiltonian and supermomenta constraints, that are preserved from the Arnowitt-Deser-Misner formulation of GR. There is a set of $\frac{n(n-1)}{2}$ primary constraints that represent the local Lorentz transformations of the theory, which can be combined to form a set of $\frac{n(n-1)}{2}-1$ first-class constraints, while one of them becomes second-class. This result is irrespective of the dimension, due to the structure of the matrix of the brackets between the constraints. The first-class canonical Hamiltonian is modified due to this local Lorentz violation, and the only one local Lorentz transformation that becomes second-class pairs up with the second-class constraint $π\approx 0$ to remove one d.o.f. from the $n^2+1$ pairs of canonical variables. The remaining $\frac{n(n-1)}{2}+2n-1$ primary constraints remove the same number of d.o.f., leaving the theory with $\frac{n(n-3)}{2}+1$ d.o.f. This means that $f(T)$ gravity has only one extra d.o.f., which could be interpreted as a scalar d.o.f.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑