# Tag Info

0

There is no $1/2$ because such factors arise whenever there are products of the same field. For example, you probably have seen the interaction term in $\phi^4$ theory written as $\frac{\lambda}{4!}\phi^4$. This is because when taking functional derivatives to get the Feynman rules, these combinatoric factors will arise from the derivative hitting any of the ...

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The assumption of a full eigensystem is usually made for convenience. But it is not always satisfied. If it is not satisfies one gets additional logarithmic contributions to the scaling laws. This is discussed, e.g., in the paper by Wegner and Riedel.

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A real scalar field has one degree of freedom...Here we have two degrees of freedom (two real scalar field) and we treat $\phi$ and $\phi^{*}$ as independent field. When we put the lagrangian in Euler-Lagrange's equation we generate a factor of 2 and 1/2 cancel it,e.g. $m^{2}\partial_{\phi}(\phi^{2})=2m^{2}\phi$..and similar for the derivative term... But ...

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There are attempts to use nonstandard analysis (e.g., Albeverio) or Colombeau algebras, but these haven't been developed very far. I haven't seen anything in terms of surreal numbers, but they may probably substitute for the infinitesimals in nonstandard analysis.

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I think Andrey Grozin's http://arxiv.org/pdf/hep-ph/0508242.pdf works quite well enough if you are looking for a general strategy to calculate the anomalous dimension of an operator. You need to somehow define $Z$, i.e. you need to develop a scheme. Now let's say you have defined your scheme or you have simply tried one of the conventional ones. The rest is ...

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A typical renormalization group flow can be thought of as a smooth vector field $\vec V(\mu)$ defined on parameter space. Starting with parameters $\vec\mu(\ell)$ at scale $\ell$, you obtain parameters at scale $\ell'$ by solving the differential equation $\frac{d\vec\mu}{d\ell}=\vec V(\vec\mu(\ell))$. The function $R$ referred to above can be thought of as ...

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