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10 votes

Photon propagator in path integral vs. operator formalism

Right off the bat, to answer your first question $\Pi^{\mu\nu}(p)$ is the Fourier transform of $\langle 0| T\{A_{\mu}(x) A_{\nu}(x') \} |0 \rangle$. Usually $\Pi^{\mu\nu}(p)$ would be referred to as ...
Josh Newey's user avatar
7 votes

Where does the energy in a fundamental interaction come from?

In your electron example, there are two problems: Although independently both electrons gain energy, you would never find two electrons close to one another to begin with, because such repulsion ...
controlgroup's user avatar
6 votes

Particles and fields

Particles and fields are different things in classical physics, whereas in quantum theory everything is a field. Speaking of particle-wave duality, i.e., that something is in the same time a field and ...
Roger V.'s user avatar
  • 60.4k
2 votes

Why does the imaginary time Euler-Lagrange equation imply the potential goes to zero at infinite imaginary time?

For the shape of the potential $V$ Ref. 1 is apparently referring to Fig. 2, i.e. the potential $V$ is assumed to have classical false vacuum, i.e. a local minimum $V(q_0)=0$ that is metastable, i.e. ...
Qmechanic's user avatar
  • 207k
2 votes

$\phi^4$ quantum fields theory with vanishing physical mass

Assume spacetime dimension $2 \leq d \leq 4$. The $\phi^4$ coupling constant $\lambda$ has mass dimension $[\lambda] = 4-d$. The one-loop mass correction is linear in $\lambda$. Given the UV cutoff ...
T.P. Ho's user avatar
  • 91
2 votes

Wave packet as a field configuration acting like a particle's wave function?

There is a mathematical equivalence between two different physical situations. The first situation is a wavepacket in a classical field. This describes some localized packet of energy in an ordinary ...
Andrew's user avatar
  • 51.2k
2 votes

QFT with massless particles

When textbooks specifically mention massless particles, they always mean renormalized mass. Unless protected by some type of symmetry, if the bare mass vanishes, the renormalized mass does not (due to ...
Prahar's user avatar
  • 26.6k
1 vote

Unitarily Inequivalent Representations

For a succinct explanation of the orthogonality of the vaccua for the van Hove model (which seems to be what the initial pdf might have been referring to), see Section 2 of this paper. Tne answer by ...
devnull's user avatar
  • 11
1 vote

Intuitive reason why bound states correspond to poles

I think this link will help you: ... if the scattering matrix $S_0(k)$ becomes infinite at some complex value of $k$, ...
JMadar's user avatar
  • 31

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