New answers tagged

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). ...
Qmechanic's user avatar
  • 202k
3 votes

Fermionic propagator

Hint: For eq. (1) to be non-trivial we must assume that $G^{ij}$ is antisymmetric in $i\leftrightarrow j$.
Qmechanic's user avatar
  • 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 ...
hft's user avatar
  • 20k
4 votes
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 ...
Prahar's user avatar
  • 26k
6 votes
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. ...
LPZ's user avatar
  • 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 $\Sigma$...
Mr. Feynman's user avatar
  • 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 ...
LPZ's user avatar
  • 11.5k
2 votes
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 ...
Hyperon's user avatar
  • 6,018
3 votes

Are loops counted twice in Feynman diagrams?

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.
Qmechanic's user avatar
  • 202k
3 votes

Are loops counted twice in Feynman diagrams?

Propagators correspond to line segments; since there are three line segments, there are three propagators. Two 'offshoots' of the vertex are covered by one propagator (the loop), but you'll notice ...
John Dumancic's user avatar

Top 50 recent answers are included