Lie point and variational symmetries in minisuperspace Einstein gravity
Lie point and variational symmetries in minisuperspace Einstein gravity
复制标题
微型超空间爱因斯坦引力中的谎言点和变分对称性
DOI：
10.1088/1751-8113/47/9/095202
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
P. Terzis
中科院分区：
文献类型：
--
作者：
T. Christodoulakis;N. Dimakis;P. Terzis
我们认为应用耦合常微分方程的对称性理论的情况下，reparametrization不变的拉格朗日二次的速度，这样的拉格朗日包含所有minisuperspace模型。我们发现，为了获得可能存在的对称生成器的最大数量，必须（a）考虑自由度之间的失效N（t）和（B）允许生成器对拉格朗日和/或运动方程的作用产生约束的倍数，而不是严格为零。对标准理论（关于正则系统）进行这种必要修改的结果是，运动方程的李点对称性恰好是变分对称性（包含时间重参数化对称性）加上众所周知的标度对称性。这些变分对称性被看作是度量和势的同时共形Killing场，因此与相空间中定义的条件对称性相一致。在一个参数化的推移，其中的潜力成为常数，上述对称性的发电机成为Killing场的标度超度规和它的位似场，分别。
We consider the application of the theory of symmetries of coupled ordinary differential equations to the case of reparametrization invariant Lagrangians quadratic in the velocities; such Lagrangians encompass all minisuperspace models. We find that, in order to acquire the maximum number of possibly existing symmetry generators, one must (a) consider the lapse N(t) among the degrees of freedom and (b) allow the action of the generator on the Lagrangian and/or the equations of motion to produce a multiple of the constraint, rather than strictly zero. The result of this necessary modification of the standard theory (concerning regular systems) is that the Lie point symmetries of the equations of motion are exactly the variational symmetries (containing the time reparametrization symmetry) plus the well known scaling symmetry. These variational symmetries are seen to be the simultaneous conformal Killing fields of both the metric and the potential, thus coinciding with the conditional symmetries defined in phase space. In a parametrization of the lapse for which the potential becomes constant, the generators of the aforementioned symmetries become the Killing fields of the scaled supermetric and its homothetic field, respectively.
影响因子：
3.5
作者：
T. Harada;M. Kimura
通讯作者：
T. Harada;M. Kimura