Uniqueness of the Fock representation of the Gowdy S1 × S2 and S3 models
Uniqueness of the Fock representation of the Gowdy S1 × S2 and S3 models
复制标题
Gowdy S1 × S2 和 S3 模型的 Fock 表示的独特性
DOI：
10.1088/0264-9381/25/10/105005
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发表时间：
2008
影响因子：
3.5
通讯作者：
J. Velhinho
中科院分区：
文献类型：
--
作者：
J. Cortez;G. A. M. Marugán;J. Velhinho
在适当的规范固定之后，Gowdy S1 × S2和S3宇宙学的局部引力自由度被编码在球面S2上的轴对称场中。最近，它已被证明，这些简化模型的标准场参数化承认没有Fock量子化与酉动力学。这种统一性的缺乏被场的方便的重新定义和适当的复杂结构的选择所克服。结果是一个Fock量子化，其中场方程的动力学和SO（3）对称性都是酉实现的。目前的工作证明，这种Fock表示实际上是唯一的，因为，直到等价，不存在其他可能的选择SO（3）不变的复杂结构，导致一个单一的实现的时间演化。
After a suitable gauge fixing, the local gravitational degrees of freedom of the Gowdy S1 × S2 and S3 cosmologies are encoded in an axisymmetric field on the sphere S2. Recently, it has been shown that a standard field parametrization of these reduced models admits no Fock quantization with a unitary dynamics. This lack of unitarity is surpassed by a convenient redefinition of the field and the choice of an adequate complex structure. The result is a Fock quantization where both the dynamics and the SO(3)-symmetries of the field equations are unitarily implemented. The present work proves that this Fock representation is in fact unique inasmuch as, up to equivalence, there exists no other possible choice of SO(3)-invariant complex structure leading to a unitary implementation of the time evolution.