Questions tagged [dimensional-regularization]
Dimensional regularization is a method of isolating divergencies in scattering amplitudes.
145 questions
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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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Why don't we use dimensional regularization in Wilsonian renormalization group?
In elementary treatments of Wilsonian approach to renormalization group (for example in Peskin & Schroeder, Srednicki, Schwartz, etc.), everybody after chapters of seemless use of dimensional ...
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Renormalization verse dimensional regularization [duplicate]
I am trying to learn QFT for fun, well past college age and have never sat in a college classroom. I understand counter terms, and how they re-normalize the Lagrangian fairly well. I understand a ...
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Meaning of Regularization
In renormalization theory, we choose a certain type of regularization method in order to study the analytic behavior of UV divergence (whether it diverges as $\lim_{\epsilon\rightarrow 0} 1/\epsilon$, ...
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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: $$ \Pi_2^{\mu \nu} = \frac{-2 e^2}{(4 \pi )^{d/2}}(p^2g^{\mu\nu}-p^{\mu}p^{\nu})\Gamma(2- \frac{d}{2}) \mu^{4-d} \...
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Polarization tensor of graviton in $d$ dimensions
Take the following tensor, that is the sum over the two polarizations of a gravitational wave in 3 spatial dimensions: $$E_{ijkl}(\vec{k})\equiv\sum_{\lambda = +,\times} \epsilon^\lambda_{ij}(\vec{k})\...
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Massless Sunset Diagram $\phi^4$ [closed]
I should compute an explicit calculation for the sunset diagram in massless $\phi^4$ theory. The integral is $$-\lambda^2 \frac{1}{6} (\mu)^{2(4-d)}\int \frac{d^dk_1}{(2\pi)^d} \int \frac{d^dk_2}{(2\...
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Massless tadpole integrals in dimensional regularization
I'm trying to prove the following: \begin{equation} \int_0^\infty x^a dx = 0, \hspace{2pt} \forall a\in \mathbb{R}. \end{equation} This should work in dimensional regularization. I found a lot of ...
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