# Tag Info

1 vote
Accepted

### The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT

$Z_0=Z[J\!=\!0]$ in eq. (9.39) is the functional determinant from the Gaussian integration of the path integral with a quadratic action. See also how P&S complete the square in eqs. (9.37)-(9.38). ...
• 202k

### Fermionic propagator

Hint: For eq. (1) to be non-trivial we must assume that $G^{ij}$ is antisymmetric in $i\leftrightarrow j$.
• 202k
1 vote

### A question about time evolution of position distributions

Then, can I describe the transform between the two distributions as $$P’(x) = \int P(a) D(a, x-a, t’, t)da$$ over all space. No. Not in general, if you want to include quantum mechanics. It is well ...
• 20k
Accepted

### Why are 2-point functions Green's functions?

It follows from the Schwinger-Dyson equations. Let's prove it for the case you're interested in (though the equations are more general). I will do it for a scalar field and let you work out the ...
• 26k
Accepted

### Exponential decay of propagator outside lightcone

Such asymptotic behaviour are typically calculated using the Laplace method (which is generalised to the saddle point method). It's worth looking into in depth, you'll use it again and again in QFT. ...
• 11.5k
1 vote
Accepted

### Renormalization condition for field strength renormalization

At any loop level, the general form of the dressed propagator of the $\phi^4$ theory is $$\tilde{D}_\text{resummed}(p)=\frac{i}{p^2-m_0^2(\Lambda)-\Sigma(p^2,\Lambda)}\tag{1}\label{1},$$ where $\Sigma$...
• 1,929
1 vote

### How does the Green's function related the wavefunctions at different space-time points in Schrödinger's equation?

In short, the link between the two is Duhamel’s principle. Green’s functions arise whenever you want to solve an inhomogeneous linear problem. In the case of the Schrödinger equation, there are two ...
• 11.5k
Accepted

### How does the Green's function related the wavefunctions at different space-time points in Schrödinger's equation?

Suppose you know the wavefunction $$\phi(t^\prime,x^\prime)=\langle x^\prime |\phi(t^\prime)\rangle \tag{1} \label{1}$$ (in the Schrödinger picture) at some (fixed) initial time $t^\prime$ and you ...
• 6,018
Well, the self-loop propagator $D(z-z)$ in OP's Feynman diagram occupies 2 of the 4 legs of the 4-vertex. It is also responsible for a symmetry factor $S=2$ that the diagram should be divided with.