New answers tagged renormalization
0
votes
Insertions of the action inside correlators
I'll do this in Euclidean space. The partition function is
$$
Z[\alpha] = \int e^{-\alpha S}
$$
Here $\alpha$ is some overall factor; could be $1/\hbar$, or inverse temperature $\beta$ depending on ...
- 91
2
votes
$\phi^4$ quantum fields theory with vanishing physical mass
Assume spacetime dimension $2 \leq d \leq 4$. The $\phi^4$ coupling constant $\lambda$ has mass dimension $[\lambda] = 4-d$. The one-loop mass correction is linear in $\lambda$. Given the UV cutoff ...
- 91
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Confusion about solution of the Callan-Symanzik Equation
I think it is just because we integrate backward in time, $t'$ is the time backward, and the "initial" concentration is $D(t, x)$, and the final concentration is $D_i(x)$ , and as time goes ...
- 56
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Beta function calculation in massless minimal subtraction $\phi^4$ theory
First: you have an incorrect sign in your $\delta_\lambda$: see, for example, David Skinner's AQFT notes. In your notation, you should have that the quartic counterterm is positive
$$
``\delta_\lambda ...
2
votes
QFT with massless particles
When textbooks specifically mention massless particles, they always mean renormalized mass. Unless protected by some type of symmetry, if the bare mass vanishes, the renormalized mass does not (due to ...
- 26.6k
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vote
Accepted
Missing counterterms in $\phi^3$ + $\phi^4$ theory in 1PI effective action
First of all, this 1PI thing is quite comparable to perturbation series. Since you use Peskin/Schroeder, check out the reference to that Coleman Weinberg potential project: Coleman and Weinberg in ...
- 106
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vote
Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory
You can choose a branch cut to evaluate the negative log if I remember correctly e.g. $\log(-x) = \log(|x|) + i \pi$. The imaginary part is related to the virtual particles going on shell. This is a ...
- 460
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Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory
...
And to be precise:
$$\tilde{\Delta }(k^2 )=\frac{1}{k^2 +m^2 -i\epsilon }\tag{14.3}$$
...
Why is (as Srednicki shows):
$$\int \frac{d^dl}{(2\pi )^d}\tilde{\Delta }((l+k)^2)\tilde{\Delta }(l^2 )$$
...
- 21.9k
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Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory
I was asked to expand my comment to an answer. Maybe it would be useful to keep in mind a more physical notion of what the loop diagrams represent.
Recall we are trying to understand our interacting ...
- 589
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What does it mean to "resum" the large logarithms?
I don't even understand what do we mean with resumming
Resummation literally means re-summation.
The one-loop
$$
\Pi(p^{2})\propto log(p^{2}/\mu^{2})
$$
is the first non-constant term if we expand $\...
- 4,452
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$\operatorname{O}(N)$ sigma model at large $N$
A couple of remarks on the comments. As mentioned already, due to the rescaling of $\lambda\to\lambda/N$ in the coupling, you are already in the analogue of the 't Hooft limit, the large $N$ limit is ...
- 13.1k
2
votes
Accepted
Role of the natural temperature scale in the anomalous dimension of the renormalization group
The usual rule $\langle\phi(x)\phi(0)\rangle\sim 1/x^{2\Delta}$ holds in $\mathbb R^d$. If the manifold has a single scale, such as $S^1\times\mathbb R^{d-1}$, this scaling is still valid, since we ...
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