Energy-momentum tensor in quantum field theory
Energy-momentum tensor in quantum field theory
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DOI：
10.1103/physrevd.23.2262
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发表时间：
1981-05
影响因子：
5
通讯作者：
K. Fujikawa
中科院分区：
文献类型：
--
作者：
K. Fujikawa
能量-动量张量作为与背景引力场耦合的源电流的定义在量子理论中得到了重要的修改。在路径积分方法中，一般坐标变换下积分测度的显协方差决定了权重为$\frac {1}{2}$的场变量应用作独立积分变量。一个改进的能量动量张量，然后产生的变分导数，它引起定义良好的引力共形（Weyl）异常。在平坦时空极限中，所有与时空变换（包括整体伸缩）相关的沃德-高桥恒等式在这个能量-动量张量方面变得没有异常，反映了积分测度的一般协变性;因此，对于可重整化理论，这个张量的迹在零动量转移处是有限的。雅可比矩阵的局部共形变换，但是，成为非平凡的，它引起了一个异常的共形身份。因此，所有熟悉的反常都归结为手征反常或共形反常。膨胀和共形恒等式在动量转移消失时的一致性决定了这个能量动量张量在重整化群$\ensuremath {\beta}$函数和其他参数方面的迹异常。相比之下，传统的能量-动量张量的轨迹通常发散，甚至在消失的动量转移取决于正则化方案，它是减重整化。我们还解释了如何明显不同的重整化性质的手征和痕迹异常出现。
The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight $\frac{1}{2}$ should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat-space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group $\ensuremath{\beta}$ function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise.