Low-energy General Relativity with torsion: a systematic derivative expansion
Low-energy General Relativity with torsion: a systematic derivative expansion
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具有挠场的低能广义相对论：系统导数展开
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Vladimirov
中科院分区：
文献类型：
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作者：
D. Diakonov;A. Tumanov;A. Vladimirov
我们试图为引力理论的爱因斯坦-嘉当公式（通常包括挠场）系统地构建低能有效拉格朗日。我们按一定的给定顺序列出所有不变的动作项；一些不变量是新的。我们证明，在主导顺序中，具有挠场的费米子作用具有额外的 U(1)L × U(1)R 规范对称性，其中 4+4 个挠场分量（一般为 24 个）扮演阿贝尔规范玻色子的角色。扭转的玻色子作用二次方为这些规范玻色子提供了质量。对扭转进行积分可得到点状 4-费米子作用，其一般形式包含矢量-矢量、轴-矢量和轴-轴相互作用。我们提出了一种量子场论方法来平均费米子介质上的 4-费米子相互作用，并在给定的化学势和温度下对自由费米子进行显式平均。结果与之前使用的“旋转流体”方法的结果不同。总的来说，我们对观察挠场引起的 4-费米子相互作用的影响的可能性得出了相当悲观的结论，尽管在某些情况下它可能会产生宇宙学后果。
We attempt to build systematically the low-energy effective Lagrangian for the Einstein–Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order the fermion action with torsion possesses additional U(1)L × U(1)R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action of a general form containing vector-vector, axial-vector and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the “spin fluid” approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.