8
votes
Accepted
Functional derivative under a path integral sign
For what it's worth, to gain some intuition, consider the following crude discretization of OP's path integral:
$$\frac{\partial}{\partial\chi^k}\underbrace{\left[\prod_{i\in I} \int d\phi^{i} e^{-{\...
- 208k
2
votes
Alternative QFT description
Describing a field as an infinite number of harmonic oscillators is another way of saying you are doing perturbation theory. For a free field, the decomposition into harmonic oscillators is exact. For ...
- 52.2k
2
votes
Why is $\phi$ not primary for 2d free boson?
You can think of it this way. Is there a local operator $\phi(x)$ which satisfies the following properties?
The rescaling $x' = \lambda x$ makes the operator transform as $\phi'(x') = \phi(x)$.
This ...
- 8,411
1
vote
Alternative QFT description
Quantum field theory on curved spacetime is a subject of active research and I don't know of any serious possibility of testing it in the near future so everything written about it should be taken ...
- 9,265
1
vote
Electron-phonon coupling within field integral formalism
Here is my attempt, which I think is sensible.
Define $g_{q} = i \gamma q_j/ \sqrt{2m\Omega_q}$ where we absorbed the $j$ index into $q$. We also stick the spin-index $\sigma$ into $k$. The phonon ...
- 111
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