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Results tagged with field-theory
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user 100922
For questions where the dynamical variables are fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). Comprises both classical field theory and quantum field theory. Use this tag when the question applies to both classical and quantum phenomena. Otherwise, use the specific tag instead.
1
vote
Accepted
Is this a right approach to show that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz ...
It's not really consistent. You're manipulating symbols in a way that doesn't make sense, especially when you bring together $c_1$, $c_2$ and $c_3$ in $c_1 c_2/c_3$. Just start by showing how
$$\frac{ …
- 1,537
1
vote
Question on the $1/N$ expansion
Your last question "Are we still not summing over all intermediate states to get the factor $N$?" is too lazy. The diagram in question has a value that is completely fixed by the Lagrangian $\mathcal{ …
- 1,537
0
votes
Why do we demand that the counterterms in $\varphi^3$ theory be $O(g^2)$?
There's a cute argument based on symmetry, at least at when $Y = 0$ is treated as a perturbation. The $g=Y=0$ theory has a $\mathbb{Z}_2$ symmetry $\phi \to -\phi$. Let $X$ be some observable that's n …
- 1,537
1
vote
Computation in QFT
At a very basic level, taking a derivative with a down (up) index gives an up (down) index. For instance, let
$$
f(v,w) = v^\mu w_{\mu} = v_{\mu} w^\mu.
$$
Then
$$
\frac{\partial f}{\partial v_\mu} = …
- 1,537
13
votes
Accepted
Can you naïvely reduce the dimensionality of a QFT?
Yes, you could consider such a dimensional reduction. The idea is to decompose $\phi(t, \mathbf{x})$ as
$$
\phi(t, r, \theta) = \sum_{k \in \mathbb{Z}} \phi_k(t, r) e^{i k \theta}.
$$
You plug this An …
- 1,537