Chern–Simons terms in metric‐affine space‐time: Bianchi identities as Euler–Lagrange equations
Chern–Simons terms in metric‐affine space‐time: Bianchi identities as Euler–Lagrange equations
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度量仿射时空中的陈-西蒙斯项：作为欧拉-拉格朗日方程的比安奇恒等式
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
E. W. Mielke
中科院分区：
文献类型：
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作者：
F. Hehl;W. Kopczyński;J. Mccrea;E. W. Mielke
引力的度规-仿射规范理论包含一个具有以下几何场的时空：同框ϑα、度规g和独立的线性连接Γαβ。在此几何框架下，构造了作为规范拉格朗日边界项的所有四种形式B=DC，即GL(4，R)标量形式以及由Chern-Simons三形式C导出的精确形式。(4.20)。翻译作品dctt是新的。边界项有效地用作非度规、挠率和曲率的比安奇恒等式的拉格朗日函数。在正则形式中，Chern-Simons三态的正规部分表示能够生成新的Ashtekar型变量的生成函数。最后，将Bach-Lanczos恒等式推广到度规仿射时空。
The metric‐affine gauge theory of gravity encompasses a space‐time with the following geometrical fields: coframe ϑα, metric g, and an independent linear connection Γαβ. Within this geometrical framework, all four‐forms B=dC are constructed which qualify as boundary terms for a gauge Lagrangian, that is, they are GL(4,R)‐scalars as well as exact forms derived from Chern–Simons type three‐forms C. The result of our search is summarized in Eq. (4.20). The translational piece dCTT is new. The boundary terms effectively serve as Lagrangians for the Bianchi identities of nonmetricity, torsion, and curvature. In the canonical formalism, the normal parts of the Chern–Simons three‐forms represent generating functions that are capable of generating new Ashtekar type variables. Eventually, the Bach–Lanczos identity is generalized to the metric‐affine space‐time.