# Tagged Questions

32 views

### The sum of positive integers equals minus one twelfth [duplicate]

I was watching a lecture online from the american physicist Lawrence Krauss, when he made an off the cuff remark about the sum of all the positive integers being equal to one twelfth. My question is ...
393 views

### Divergent Series

Why is it that divergent series make sense? Specifically, by basic calculus a sum such as $1 - 1 + 1 ...$ describes a divergent series (where divergent := non-convergent sequence of partial sums) ...
2k views

### How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”? [duplicate]

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics? I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis ...
115 views

### Not satisfied with “trick” in zeta function regularization

I am not satisfied with the explanations of the $\sum_n \log \lambda_n = - \frac{d}{ds} \sum_n \lambda_n^{-s}|_{s=0}$ "trick" used in zeta function regularization, discussed here and here, or the ...
144 views

### Delta functional in path integral

I've recently encountered a path integral of the form $$\int \delta[a\phi+b\phi']\,L(\phi,\phi')\;\mathcal D\phi\mathcal D\phi'$$ (where $a$, $b$ are integers) and would like to eliminate one of the ...
111 views

### Confused by renormalization [duplicate]

Possible Duplicate: Suggested reading for renormalization (not only in QFT) I'm trying to learn QFT. I don't quite understand why renormalization works. If you are calculating a Feynman ...
3k views

### Don't understand the integral over the square of the Dirac delta function

In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on ...
223 views

### Gaussian type integral with negative power of variable in integrand

How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course Mathematical Tools for Physics. Can a situation ...
344 views

### Is the step of analytic continuation unavoidable or can you model around it?

One sometimes considers the analytic continuation of certain quantities in physics and take them seriously. More so than the direct or actual values, actually. For example if you use the procedure ...
135 views

### Functional determinant approximation

Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$. I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use \sum_{n} ...
293 views

### How are functional determinants of Laplace-type operators used in physics?

Many mathematical papers concerning the $\zeta$-regularized Determinant of Laplace-type operators refer for motivation to the broad use of such determinants in mathematical physics, especially in ...
723 views

### Is QFT mathematically self-consistent?

After recently going through a short program of self-study in quantum mechanics, I was surprised to find a quote attributed to Feynman essentially saying he was extremely bothered by the computational ...
214 views

### Other processes than formal power series expansions in quantum field theory calculations

I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e. , what dynamical systems ...
336 views

I have some questions about Pade approximants. Given a divergent power series $\sum_{n >0} a(n)x^{n}$ can we use a Pade Approximant to it $R(x)$ so we can obtain a SUM of the series for every ...
797 views

### Are there books on Regularization and Renormalization in QFT at an Introductory level?

Are there books on Regularization and Renormalization, in the context of quantum field theory at an Introductory level? Could you suggest one? Added: I posted at math.SE the question Reference ...
548 views

### Iterated dimensional regularization

Given a 2-loop divergent integral $\int F(q,p)\,\mathrm{d}p\mathrm{d}q$, can it be solved iteratively? I mean I integrate over $p$ keeping $q$ constant Then I integrate over $q$ In both iterated ...
2k views

### Limit of Lorentzian is Dirac Delta

I have a quick question that just came up in my research and I could not find an answer anywhere so I thought I'd try here. So one of the definitions of the Dirac Delta is the limit of the Lorentzian ...
1k views

### Laplacian of $1/r^2$ (context: electromagnetism and poisson equation)

We know that a point charge $q$ located at the origin $r=0$ produces a potential $\sim \frac{q}{r}$, and this is consistent with the fact that the Laplacian of $\frac{q}{r}$ is ...