Questions tagged [dimensional-regularization]
Dimensional regularization is a method of isolating divergencies in scattering amplitudes.
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Expressing Feynman Integrals Using Schwinger Parameterization
I am trying to practice the techniques given in the book "Feynman Integrals: A Comprehensive for Students and Researchers," by Stefan Weinzierl (preprint). I am getting stuck on one point ...
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Formal definition of $d$-dimensional integral for complex dimension $d\in\mathbb{C}$
This question concerns the definition of dimensional regularization in quantum field theory, specifically as presented in this Wilson paper (see free version here).
This operation must fulfill three ...
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A basic trick $k^\mu k^\nu=\frac14g^{\mu\nu}k^2$ when calculating Feynman integrals [duplicate]
I am reading Schwarz's book "Quantum Field Theory and Standard Model", chap 17, anomalous magnetic moment. In 17.2, page 319, when simplifying the integral, the book says "Using $k^\mu ...
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"Naturalness" of the 't Hooft-Veltman-Breitenlohner-Maison (HVBM) scheme in Dimensional Regularization
Disclaimer: This question is fairly subjective based on what one considers a natural construction. With that in mind, let's continue.
I'm trying to understand more complicated examples of dimensional ...
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Renormalization Scheme on Peskin and Schroeder Page 409
On page 409 of P&S book, they are basically considering the subtraction scheme of the scalar field propagator in Yukawa theory, see the figure below.
Write explictly, it is:
$$
\frac{4ig^2}{(4\pi)...
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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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Is there a way to generalize the classical electromagnetic field strength tensor to arbitrary (possibly non-integer) dimensions?
is there a way to generalize the electromagnetic field strength tensor to general, specifically non-integer dimensions? As context: I am currently working on a calculation in the high energy QFT ...
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Solving second-order differential equation for inflationary fields in the late-time limit
I need your help guys. I have been reading this paper by Weinberg hep-th/0506236, and I am stuck in figuring out how he wrote the solution of some differential equations for various inflationary ...
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What regularization gives the physical solution?
I am not an expert on Hadamard regularization/Dimensional regularization, I am still learning. I am recovering some locally diverging integral, for a physical solution I need to use Hadamard part ...
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Where does the $\pi^2$ term come from in this Feynman diagram?
I am looking at this paper on anomalous magnetic moment. Trying to go through the calculations. The first graph 1a on p. 1070 seems to be the "easiest" as it requires no renormalization and ...
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Understanding Dimensional Regularization
I am diving into the potential minefield that is learning regularization and renormalization, and I am currently lost on dimensional regularization. I understand the intuitive idea using dimension as ...
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Help with doing a Feynman 1-loop integral related to $\langle T_{++}\rangle$ in string theory
The goal is to compute the 1-loop integral, which is given equal to:
$$\int{\frac{d^2l}{2\pi}\frac{l_{+}(l_++q_+)}{l^2(l+q)^2}}=-\frac{1}{4}\frac{q_+}{q_{-}}.\tag{3.31}$$
The above integral represents ...
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One-loop diagrams for the Yukawa pseudo-scalar interaction
I have a Lagrangian describing a pseudo-scalar Yukawa interaction. This Lagrangian has a dimension $d=4-2\eta$. Here it is:
$$\mathcal{L} = \frac{1}{2}(\partial_\mu \phi)(\partial^\mu \phi) - \frac{1}{...
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How to compute this integral in dimensional regularisation?
I'm trying to compute the following position space integral as a function of $d$, which should be finite for $2<d<4$:
$$ I=\int \frac{d^d y \, d^d z}{ \left( |x-y| \,|y_\perp|\,|y-z|\,|z_\perp|\,...
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Some calculation in Schwartz's Quantum field theory eq. (16.39)
In Schwartz's Quantum field theory and the standard model, p.307 he derives a formula:
$$ \Pi_2^{\mu \nu} = \frac{-2 e^2}{(4 \pi )^{d/2}}(p^2g^{\mu\nu}-p^{\mu}p^{\nu})\Gamma(2- \frac{d}{2}) \mu^{4-d} \...
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