# Questions tagged [regularization]

In QFT, regularization is a method of addressing divergent expressions by introducing an arbitrary regulator, such as a minimal distance *ϵ* in space, or maximal energy *Λ*. While the physical divergent result is obtained in the limit in which the regulator goes away, *ϵ* → 0 or *Λ* → ∞, the regularized result is finite, allowing comparison and combination of results as functions of *ϵ, Λ*. Use for dimensional regularization as well.

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### $\varphi^4$ via renormalization group with hard cut-off

I am studying the application of the renormalization group to the $\varphi^4$ theory: $$\mathcal{L} = -\frac{1}{2} \varphi (\Box + m^2)\varphi -\frac{\lambda}{4!}\varphi^4.$$ In particular I wanted to ...
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### Why is renormalization (instead of regularization) is needed in QFT?

This question looks like a duplicate question but I will try to make it different. In QFT, since divergence arise in the calculation of some quantities, we need regularization to remove the ...
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### Integral divergent in Peskin and Schroeder eq. (7.90)

I'm working on the Eq. (7.90) in Peskin (page 252). However, I don't understand why it diverges logarithmically. Does $\Gamma(0)$ mean logarithmically divergence?
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### Polchinski massless vertex operator in the Polyakov approach p105 Eq. (3.6.16)

I am trying to check the Weyl transformation of the massless vertex operator in Polchinski closed bosonic string in the Polyakov approach (p105, Eq 3.6.16).To do that one needs to calculate something ...
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I need to determine Feynman one-loop integrals to work out some Feynman diagrams, in particular $I_{2,1}$. Starting from the general formula: $$I_{n,m}=\frac{1}{(4\pi)^2}\frac{\Gamma(m+2-\frac{\... 1answer 63 views ### Convergence of the path integral In P&S 9.3 the path integral$$ Z[J]=\int {\cal D}\phi \exp[i\int d^4x ({\cal L} + J\phi)]$$of the (Minkowski) \phi^4-theory when subjected to a Wick-rotation (change of the integration path ... 1answer 68 views ### How can I relate this integral to dimensional regularization? In the paper "Scattering into the Fifth Dimension of \mathcal{N}=4 Super Yang-Mills", the authors give the following result for an integral:$$\begin{align} I^{(1)}(x_{13}^2,x_{24}^2,m) =& \...
When we try to regulate a divergent integral, we introduce another parameter, say $\lambda$ and then compute the integral. We finally take a limit (either $\lambda \rightarrow 0, \infty$) to restore ...