Schrödinger representation for the polarized Gowdy model
Schrödinger representation for the polarized Gowdy model
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DOI：
10.1088/0264-9381/24/1/001
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发表时间：
2006-07
影响因子：
3.5
通讯作者：
C. Torre
中科院分区：
文献类型：
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作者：
C. Torre
在标准规范下，极化T3 Gowdy模型具有点粒子自由度和服从R × S1上线性场方程的标量场自由度。标量场的Fock表示已经得到了很好的研究。我们用高斯概率测度的分布场空间上的平方可积函数构造了Gowdy时间固定值下标量场的Schrödinger表示。我们证明了“典型”场构型比圆上的平方可积函数稍微奇异一些。对于每一次，对应的Schrödinger表示都与Fock表示一元等价，因此所有的Schrödinger表示都是等价的。然而，该模型的时间演化不具有统一可实现性，表现为高斯测度在不同时刻的相互奇异性。
The polarized T3 Gowdy model is, in a standard gauge, characterized by a point particle degree of freedom and a scalar field degree of freedom obeying a linear field equation on R × S1. The Fock representation of the scalar field has been well studied. We construct the Schrödinger representation for the scalar field at a fixed value of the Gowdy time in terms of square-integrable functions on a space of distributional fields with a Gaussian probability measure. We show that ‘typical’ field configurations are slightly more singular than square-integrable functions on the circle. For each time the corresponding Schrödinger representation is unitarily equivalent to the Fock representation, and hence all the Schrödinger representations are equivalent. However, the failure of unitary implementability of time evolution in this model manifests itself in the mutual singularity of the Gaussian measures at different times.