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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Axial anomaly using dimensional regularization
I am looking for papers or references where the axial (Adler–Bell–Jackiw) anomaly is computed explicitly using dimensional regularization by evaluating the triangle diagram.
Most treatments in ...
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Regularizing scattering amplitudes by puncturing the complex plane
When working with complex functions, as is typically the case in scattering theory, one often encounters the function under study has a discrete set of poles. The residue theorem allows us to ...
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Fermion determinant with Hurwitz Zeta function
Consider the Euclidean path integral for the partition function of a fermionic harmonic oscillator
$$ Z(\beta) = \int \mathscr{D}\psi^{\dagger} \mathscr{D} \mathscr{\psi} \, e^{i \int_{0}^{\beta} d\...
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Zeta function regularization of the trace of the identity operator
Consider the identity operator of the $1D$ quantum harmonic oscillator $$\mathbf{I} = \sum_{n=0}^{\infty}|n\rangle\langle n|$$
If I take trace of the above I get
$$\operatorname{tr}(\mathbf{I}) = \...
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Pauli-Villars regularization made simple
I'm studying scalar quantum field theory. If I understood correctly, when applying Pauli-Villars regularization I replace the propagator with
$$
\frac{1}{k^2 + m^2} \rightarrow
\frac{1}{k^2 + m^2} + \...
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What is the difference between an ultraviolet limit and ultraviolet stability?
One common way to analyze a quantum field theory is to regularize it by introducing an ultraviolet cutoff. After perhaps renormalizing the theory, one would hope that you can remove the cutoff by ...
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Point-splitting regularization for ghost fields
In section V of this paper, the author computes $\langle F_{\mu \nu} F^{\mu \nu} \rangle$. Using the definition of $F_{\mu \nu}$ it is not difficult to show that
$$\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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