β Scribed by Lowell S Brown
No coin nor oath required. For personal study only.
Techniques of dimensional regularization are discussed in the context of scalar field theory. After reviewing the method and its connection with the renormalization group, we present explicit forms for the relationship between bare and renormalized composite operators of low dimensionality. These results show that a suitably improved stressenergy tensor is finite, for it can be written as a combination of renormalized composite operators with finite numerical coefficients. We thereby derive in a simple way the previously known trace anomaly. The trace of the stress-energy tensor describes the breaking of dilation invariance and yields an alternative derivation of the renormalization group equations. The trace also describes the breaking of special conformal invariance, but this leads to equations involving composite operator insertions in contrast to the closed differential equations of the renormalization group.
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