# 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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### Calculating the transition amplitude

Lagrangian of the Lee-Yang model is given by: $$L=\frac{1}{2}f(q)\dot{q}^2$$ where $f(q)$ is some differentiable function. I am trying to derive the following expression for the transition ...
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### What is a logarithmic divergence?

I am reading about renormalisation in QED and I come across the term logarithmic divergence several times. Can somebody explain to me about it in simple terms?
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### How do we know that analytic continuation agrees with UV regulators?

Consider the divergent series $$S = 1 + 1 + 1 + \ldots$$ which may appear in some calculations involving the Casimir effect. There are two main ways to evaluate this series. One can perform analytic ...
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### Why Does Renormalized Perturbation Theory Work?

I've read about renormalization of $\phi^4$ theory, ie. $\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-m^2\phi^2-\frac{\lambda}{4!}\phi^4\,,$ particularly from Ryder's book. But I am ...
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### Divergent diagrams in QED

I was reading about how to choose divergent diagrams in QED by using the concept of Superficial degree of divergence. We have an empirical relation $$D= 4-E_b -\frac{3}{2}E_f$$ where $E_b$ is number ...
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### Quantization of free real scalar massless field in 2d

Is there a reference to literature where one explicitly constructs quantization of the free real scalar massless field in the 2-dimensional space-time? In particular, how the propagator looks like? ...
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### Dependence on UV cut off of some $\phi^4$ diagrams

Consider the one loop corrections to the propagator and the vertex in $\phi^4$-theory:                    &...
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### Size of box vs. discrete-ness of state of the system

From Statistical Physics, 2nd Edition by F. Mandl, pg. 36: A sufficiently large box (say 10 light-years across) will clearly not affect the properties of our system, ion plus electron sitting ...
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### Representing propagators as Dirac delta functions [closed]

I have found online, in particular on the wolfram site, http://mathworld.wolfram.com/DeltaFunction.html, certain identities that allow one to represent a delta function as limits. Of particular ...
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### Is this charge density function, from a problem in Griffiths' book, a physically valid density?

This is from the book on electrodynamics by Griffiths: A sphere of radius $R$, centered at the origin, carries charge density $$\rho(r,\theta)= k(R/r^2)(R-2r)\sin(\theta)$$ where $k$ is ...
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### What is the reason/significance of using $\sum\limits_{n=1}^{\infty}n\rightarrow-\frac{1}{12}$?

What is the reason/significance of using a trick equation in the Volume I - String Theory - Joseph Polchinsky? I have no doubts at all that the author knows extremely well the subject and that this ...
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### Regularization of the 1-dimensional Laplacian

Disclaimer: this is a technical question about regularization of functional determinants which comes from a person with (relatively) strong background in QFT, string theory and path integrals, who ...
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### How to handle the infrared divergence of massless $\phi^4$ in scattering

For massless $\phi^4$ theory, if exterior momentums are going to zero, then this diagram will be $$\int \frac{dk^4}{k^4}$$ will suffer from infrared divergence. Because the infrared divergence, ...