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Physics

Questions tagged [regularization]

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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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In section V of this paper, the author computes $\langle F_{\mu \nu} F^{\mu \nu} \rangle$. Using the definition of $F_{\mu \nu}$ it is not difficult to show that$$\langle F_{\mu \nu} F^{\mu \nu}\...
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Calculations are carried out in Euclidean plane with complexified coordinates $z,\bar{z}$ as we do in CFT. I need to derive the following:$$\int{\frac{d^2 z_1}{(z-z_1)(\bar{z_1}-\bar{w})}}=\pi\ln{|z-...
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My question concerns this paper. Here, the author defines point split fermion bilinears as$$ J_{\Gamma_A}(x,\epsilon) = \frac{1}{2}\left( \bar \psi(x+\epsilon) \Gamma_A \psi(x) + \bar \psi(x) \...
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I have some issues with the mathematical formalism of bosonization. In particular I'm failing to solve the exercise in Shankar's book; cfr: http://home.ustc.edu.cn/~gengb/210110/Shankar_Bosonization....
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There are many exact solutions to the simplified Navier-Stokes equations. However smooth and 3d solutions do still remain elusive.Is there a way to construct an exact 3d smooth solution generator of ...
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I had a course on QFT some years ago where renormalization was introduced but not very well motivated. It was basically introduced as a consequence of the divergence arising in the integrals when one ...
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The title might be confusing, so let me explain.Planck unknowingly started the field of quantum mechanics when he described blackbody radiation spectra using a law that assumes discrete values for ...
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Theoretically, the vacuum energy is obtained by summing over zero point energies of all the modes:$$E=\frac 12\hbar\sum_n\omega_n$$Where the modes $\omega_n$ are the eigenfrequencies of our system, ...
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I have a question regarding regularization in quantum field theory. Hagen Kleinert talks about analytic regularization in his book "Path Integrals". In chapter 2.15 he calculates the ...
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I have technical difficulties computing one-loop amplitude.My propagator have the form$$A(q,\Omega)=\int_0^\infty dk \int_{-1}^1 dx (g(q,\Omega,k,x))$$$x$ is the $\cos(\theta)$ between the ...
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In particle physics, we often encounter correlators $\Pi(q^2)$ which are functions of the squared momentum transfer $q^2$. These functions are real-valued for some $q^2$ below a threshold $M^2$, and ...
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Conventions:$\bullet\ $ Everything is expressed in lightcone coordinates defined as$$\sigma_{\pm}=\frac{1}{\sqrt{2}}(\sigma_{1}\pm\sigma_{2})$$$\bullet\ |\sigma_{12}|$ is the distance between two ...
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I'm learning renormalization in QFT, and find the following question: Use QED as example, when we do the renormalized perturbation theory, we introduce new parameters $m$ and $e$, and write the bare ...
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I have read the renormalization chapters of several QFT books, but I am still highly, deeply confused about some discussion of renormalization conditions and schemes (and some book didn't even offer a ...
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The question is about the treatment of the two-point and one-point amplitudes in linear sigma model in P&S Chapter 11.2When evaluating the one-point $\sigma$ amplitude, we encountered the diagram ...

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