Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics
Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics
复制标题
量子力学中作为微分同胚反常的相空间广义协方差的破坏
DOI：
10.1007/jhep10(2010)054
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发表时间：
2010
影响因子：
5.4
通讯作者：
Nikolay Dedushenko
中科院分区：
文献类型：
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作者：
Nikolay Dedushenko
考虑了由相空间路径积分描述的拓扑量子力学，并研究了Kontsevich公式的路径积分表示的一维模拟。我们看到，朴素玻色积分具有发散性，它甚至是朴素非不变的，因此是不好定义的。然后，我们考虑一个超扩展的理论，消除了分歧，使理论天真不变。这种超扩张等价于测度的正确选择，并在文献中进行了讨论。然后，我们调查的行为，这个扩展的理论下的扩展相空间的同胚，尽管它的朴素不变性发现，该理论具有非线性同胚下的异常。我们本地化的异常的起源，并计算出最低的非平凡异常的贡献。
We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula. We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined. We then consider a superextension of the theory which eliminates the divergences and makes the theory naively invariant. This super-extension is equivalent to the correct choice of measure and was discussed in the literature. We then investigate the behavior of this extended theory under diffeomorphisms of the extended phase space and despite of its naive invariance find out that the theory possesses anomaly under nonlinear diffeomorphisms. We localize the origin of the anomaly and calculate the lowest nontrivial anomalous contribution.