Beyond Einstein–Cartan gravity: quadratic torsion and curvature invariants with even and odd parity including all boundary terms
Beyond Einstein–Cartan gravity: quadratic torsion and curvature invariants with even and odd parity including all boundary terms
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超越爱因斯坦-嘉当引力：具有偶数和奇数宇称的二次挠率和曲率不变量，包括所有边界项
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
F. Hehl
中科院分区：
文献类型：
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作者：
P. Baekler;F. Hehl
最近，越来越多的作者从经典和量子场论的角度讨论了具有挠率的引力规范理论。爱因斯坦-卡坦(-肖马-基布尔)拉格朗日因奇偶称伪标量曲率(Hojman，Mukku和Sayed)以及扭转平方和曲率正方形而丰富，奇偶宇称也是如此。(I)我们证明了如果包含扭方块，由于拓扑的Nieh-yan形式，所谓的Barbero-Immirzi参数乘以伪标量曲率的逆可以适当地讨论。(Ii)Obukhov等人和Baekler等人提出的具有两个奇偶的二次规范拉格朗日也出现在Diakonov等人的框架内。通过在Riemann-Cartan空间中首次用曲率张量的不可约片段表示的拓扑欧拉形式和Pontryagin形式，我们建立了这两种方法之间的精确关系。(Iii)在Riemann-Cartan时空中，即在有挠率的时空中，宇称破坏项可以以直接和自然的方式引入引力拉格朗日。因此，Riemann-Cartan时空是手征费米子物质场的自然栖息地。
Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein–Cartan(–Sciama–Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero–Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh–Yan form, can be appropriately discussed if torsion square pieces are included. (ii) The quadratic gauge Lagrangian with both parities, proposed by Obukhov et al and Baekler et al, emerges also in the framework of Diakonov et al. We establish the exact relations between both approaches by applying the topological Euler and Pontryagin forms in a Riemann–Cartan space expressed for the first time in terms of irreducible pieces of the curvature tensor. (iii) In a Riemann–Cartan spacetime, that is, in a spacetime with torsion, parity-violating terms can be brought into the gravitational Lagrangian in a straightforward and natural way. Accordingly, Riemann–Cartan spacetime is a natural habitat for chiral fermionic matter fields.