# 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.

417 questions
Filter by
Sorted by
Tagged with
80 views

### Gauss' law in the presence of surface charges [duplicate]

Assume $V$ is a volume such that $\rho=0$ in $V$ where $\rho$ is the charge density. Assume further that we have a surface charge density $\sigma$ on the surface $S$ enclosing $V$ such that the total ...
• 149
48 views

### Charge density of Hertzian dipole

I am wanting to find the charge density of an infinitely thin Hertzian dipole, but am struggling evaluating the Dirac delta functions gradient. $$\vec{J} = I_{0}\cos(\omega t) \delta^3(r) \hat k.$$ ...
• 3,607
44 views

### Why does normal-ordering ensure finiteness?

I will be using Jan von Delft's rigorous construction of bosonization/refermionization as an example, but I will try to explain my question in more general terms. Consider an (countably) infinite-dim (...
• 1,598
145 views

• 273
68 views

### Regularization of a sum

I am computing the partition function of a gluon gas and I have been incurred in the following sum $$\sum_{k=0}^\infty (2k+1)^4\ln(2k+1).$$ It is clearly divergent. Is there any possible way to ...
• 3,592
618 views

### Water wave analog of Casimir effect — Does it involve the zeta function? If not, why do QED calculations involve the zeta function?

It is known that the Casimir effect has a water wave analog from classical wave theory. See also this video for a demonstration. In what ways are the calculations for the effect in QED and the effect ...
• 5,220
1 vote
36 views

### Fourier transform of Wick rotated functions

I am learning the imaginary time formalism of thermal field theory / reviewing the Euclidean formalism of quantum field theory. One thing that appears to be left implicit in many treatments is a ...
50 views

### What is the Cauchy principal value in Sokhotski-Plemelj formula?

I met the Sokhotski-Plemelj formula in a paper: in which $P$ is the Cauchy principal value. But the principal value in wiki is this form: It is a limit of an integration. But the $P$ in the first ...
32 views

### Slicing momentum cutoff

Consider the following propagator: $$C_{\kappa}(x-y) = \frac{1}{(2\pi)^{2}}\int dp \frac{-i\not{p}+m^{2}}{p^{2}+m^{2}}\chi_{\kappa}(p)e^{ip(x-y)}$$ where $\chi_{\kappa}$ is a cutoff function. If we ...
• 487
477 views

### Computing a Gaussian path integral with a zero-mode constraint

I have the following partition function: Z=\int_{a(0)=a(1)} \mathcal{D}a\,\delta\left(\int_0^1 d\tau \,a -\bar{\mu}\right)\exp\left(-\frac{1}{g^2}\int_0^1d\tau\, a^2\right) \end{...
2k views

• 3,791
1 vote
86 views

72 views

### What justifies regularization with a high-momentum cutoff?

Before renormalizing a perturbative series, during the regularization step when we insert a high-momentum UV cutoff, what justifies this step given that it's only formal and does not have a physical ...
• 569
167 views

### Multiplying distributions for QFT

My understanding is that UV divergences arise due to improperly handling the product of distributions. In what sense is it "improper"? And how does its proper handling relate to the notion ...
• 569
51 views

### Why doesn't the gluon fusion channel for Higgs production diverge?

The heavy quark triangle integral has a superficial degree of divergence of $D=1$, so one would naively expect it to diverge (more than logarithmically, in fact) in 4 dimensions. It happens, though, ...
• 1,343
1 vote
33 views

### Could the divergences in loop Feynman diagrams be resolved by applying an exponentially decreasing probability eg fluctuation theorem?

Since the divergence originates from having to integrate over an infinite range of intermediate energies, surely the bigger the temporary energy delta, the less likely it will be, and the shorter the ...
• 11
839 views

### What does mathematical consistency in QFT mean?

My question is more naive than Is QFT mathematically self-consistent? Just when people talk about the mathematical consistency of QFT, what does consistency mean? Do people want to fit QFT into ZFC? ...
• 131
119 views

### Negative potential infinite square well

A 1D finite square well is generally defined either by $$V(x)=\begin{cases} 0\qquad -a\leqslant x\leqslant a\\ V_0\qquad \text{otherwise} \end{cases} \tag{1}$$ or \begin{...
• 556
134 views

### QFT and divergences: what makes the finite part be regularization-independent?

It seems that the "finite part" of divergent loop integrals are the same, irrelevant of the regularization scheme used to regulate the integrals - why is this? Consider the following ...
• 3,141