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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Zeta-function regularization of constant product
I want to calculate a functional determinant coming from a Gaussian path integral with operator Matrix $M$. The determinant is given by the product over the eigenvalues according to $$\text{det}(M) = \...
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More than one way of renormalization for the same Feynman loop integral? [duplicate]
My understanding for renormalization is that to deal with the divergence appeared in loop integrals, we introduce an artificial regularization parameter to make the integral converge, and when we take ...
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Is the Trotter formula justified in a theory that requires renormalization?
Usually, when QFT textbooks attempt to prove the equivalence of the path integral formulation with more familiar matrix mechanics, we make use of the Trotter formula. In Euclidean time, with $\hat{H}=\...
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Singularity in the propagator in non-relativistic quantum mechanics [duplicate]
The propagator in non-relativistic quantum mechanics is: $$G(\mathbf{x}, t; \mathbf{x}', t') = \left\langle \mathbf{x} \Big| e^{-i H (t - t') / \hbar} \Big| \mathbf{x}' \right\rangle.$$ Adding the ...
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Are measurable path integral Monte-Carlo correlation functions finite?
I am thinking about the correlation functions measured in path integral Monte-Carlo (PIMC) simulations. The Wick rotation $t \to -i\tau$ formulates the two-point correlation function $\langle \phi(...
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Why is electron self-energy infrared divergent?
I'm studying QED from Mandl and Shaw's book. My question regards the regularization of the fermion self-energy correction $$ ie_0^2\Sigma(p) = \int_{\mathbb{R}^4} \frac{\text d^4 k}{(2\pi)^4} i\frac{(...
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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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Massive Gluon Regularization resources
I am trying to learn about other regularization schemes in QFT and I came across massive gluon (MG) regularization scheme in Sections 2.5, 2.6, and 2.7 of [1]. However, the presentation is very non-...
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Finding a rigorous approach to the Delta function well as a limiting case of the infinite square well
I'm having trouble finding rigorously the delta function well potential as a limiting case of the finite square well. I defined the potential in the following way $$V_\epsilon (x) = \left\{ \begin{...
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Regulating certain integral
I am interested in regulating an integral of the type, \begin{equation} I = \frac{1}{2\pi^2}\int_0^\infty p^2\ dp\ \frac{g(p)}{p^2 - k^2 - i\epsilon} = \frac{1}{4\pi^2}\int_{-\infty}^\infty p^2\ dp\ ...
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Regularization scheme preserving conformal symmetry?
I am doing some perturbative calculation on some conformal field theory like ${\cal N}=4$ SYM in $D=4$. For the not-protected correlators, some divergence might occur. However, usual regularization ...
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The path integral representation of the transition amplitude between the vacua of two field theories
The background of the question: PhysRevLett.115.261602. $ \newcommand\ket[1]{| #1 \rangle} \newcommand\braket[1]{\left\langle{#1}\right\rangle} \newcommand\dif{\mathrm{d}} \newcommand\E{\mathrm{e}} $...
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Renormalisation in rigorous algebraic formulation of QFT
Before I get to the point, let me quickly describe the context and what level of understanding I’m trying to achieve, if possible. I’d like to get some intuition on more rigorous approaches of QFTs, ...
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What rational zeta series with non-integer arguments appear in physics - if any?
Background Rational zeta series are series of the form $$\sum_{n=2}^{\infty} q_{n} \zeta(n + p, m), \label{1} \tag{1} $$ where $\zeta(x,m)$ is the Hurwitz zeta function and $q_{n}, \ p \in \mathbb{Q} \...
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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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