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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Point-splitting regularization for ghost fields
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
$$\langle F_{\mu \nu} F^{\mu \nu}\...
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Integrals in Euclidean plane with complexified coordinates?
Calculations are carried out in Euclidean plane with complexified coordinates $z,\bar{z}$ as we do in CFT. I need to derive the following:
$$\int{\frac{d^2 z_1}{(z-z_1)(\bar{z_1}-\bar{w})}}=\pi\ln{|z-...
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Are Schwinger terms always $c$-numbers?
My question concerns this paper. Here, the author defines point split fermion bilinears as
$$ J_{\Gamma_A}(x,\epsilon) = \frac{1}{2}\left( \bar \psi(x+\epsilon) \Gamma_A \psi(x) + \bar \psi(x) \...
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Bosonization and refermionization
I have some issues with the mathematical formalism of bosonization. In particular I'm failing to solve the exercise in Shankar's book; cfr: http://home.ustc.edu.cn/~gengb/210110/Shankar_Bosonization....
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Is it possible to construct Smooth solutions for the unsimplified version of the viscid and incompressible Navier-Stokes eqs.? Smooth is essential
There are many exact solutions to the simplified Navier-Stokes equations. However smooth and 3d solutions do still remain elusive.
Is there a way to construct an exact 3d smooth solution generator of ...
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Does Wilsonian renormalisation allow to send the UV cutoff to $\infty$?
I had a course on QFT some years ago where renormalization was introduced but not very well motivated. It was basically introduced as a consequence of the divergence arising in the integrals when one ...
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Does QFT predict that the lattice constant of the universe is zero?
The title might be confusing, so let me explain.
Planck unknowingly started the field of quantum mechanics when he described blackbody radiation spectra using a law that assumes discrete values for ...
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Choice of regulators in vacuum energy calculations
Theoretically, the vacuum energy is obtained by summing over zero point energies of all the modes:
$$E=\frac 12\hbar\sum_n\omega_n$$
Where the modes $\omega_n$ are the eigenfrequencies of our system, ...
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Regularization of determinants in QFT
I have a question regarding regularization in quantum field theory. Hagen Kleinert talks about analytic regularization in his book "Path Integrals". In chapter 2.15 he calculates the ...
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Divergences in series expansion of loop amplitude
I have technical difficulties computing one-loop amplitude.
My propagator have the form
$$
A(q,\Omega)=\int_0^\infty dk \int_{-1}^1 dx (g(q,\Omega,k,x))
$$
$x$ is the $\cos(\theta)$ between the ...
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Dispersion relation for heavy quark correlator
In particle physics, we often encounter correlators $\Pi(q^2)$ which are functions of the squared momentum transfer $q^2$. These functions are real-valued for some $q^2$ below a threshold $M^2$, and ...
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How to define expectation value when operators are inserted at the same point?
Conventions:
$\bullet\ $ Everything is expressed in lightcone coordinates defined as
$$\sigma_{\pm}=\frac{1}{\sqrt{2}}(\sigma_{1}\pm\sigma_{2})$$
$\bullet\ |\sigma_{12}|$ is the distance between two ...
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Understanding renormalization schemes
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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Is renormalization indeed a mathematical trick?
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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Question about the mathematical treatment in P&S Chapter 11.2
The question is about the treatment of the two-point and one-point amplitudes in linear sigma model in P&S Chapter 11.2
When evaluating the one-point $\sigma$ amplitude, we encountered the diagram ...
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