All Questions
6
questions
4
votes
2
answers
2k
views
QFT generating functional and Green function and propagator
I am confused about why does the generating functional gives the propagator by differentiation, and why that propagator is the Green function.
I understand how to take the functional derivative like ...
- 232
1
vote
0
answers
159
views
Connected part of $S$-matrix generating functional
I am currently studying an article by A.Jevicki et. al. (https://doi.org/10.1103/PhysRevD.37.1485) and I am a little confused. They say that the generating functional of the $S$-matrix is related to ...
- 93
2
votes
0
answers
148
views
Physical meaning of $\langle 0|S(+\infty,-\infty)|0 \rangle$
when I am reading text book Introduction to Many body physics Piers Coleman 2nd editor, Equation (5.26). I got confused about the meaning of $\langle0|S(+\infty,-\infty)|0\rangle$.
first problem
$|...
- 1,113
2
votes
1
answer
612
views
Explicit calculation of the two-point function by path integrals
I need help carrying out the following calculation:
We have the generating functional of free theory:
$$Z[f] = \exp\left(\frac{i}{2} \int d^4xd^4y f(x)f(y)\Delta(x-y)\right) $$
where $f$ is an ...
- 184
1
vote
0
answers
512
views
Green Function generating functional and Fourier transform spaces
I am given the transform of the generating functional for free Klein-Gordon theory,
$$Z[J]=N\int D\phi \, e^{i\int d^4 J(x)\phi(x)}\tilde{Z}[\phi]$$ where $\phi(x)$ is a scalar field. I'm a little ...
- 639
4
votes
1
answer
465
views
Physical interpretations of the generating functions $Z[J]$ and $W[J]$ (or $E[J]$)
In quantum field theory, the generator of all Green's functions $Z[J]$ and that of the connected Green's functions $E[J]$ are related as $$Z[J]=\exp[-iE[J]]=\int D\phi\exp[i\int d^4x(\mathcal{L}(\phi)+...
- 26.8k