All Questions
10
questions
2
votes
1
answer
80
views
Why does $S$-matrix theory end up being a covariant formalism when it is not obvious that it is?
A principle of QFT that is frequently invoked, repeated, and potentially subject to rigorous verification is that the theory in question must exhibit Lorentz covariance and be invariant under the ...
- 1,640
2
votes
1
answer
127
views
Why do the eigenvalues of the 4-momentum operator organize themselves into hyperboloids?
Specifically I'm asking for the motivation behind figure 7.1 in page 213 of the QFT textbook by Peskin and Schroeder. In that section they just consider eigenstates of the 4-momentum operator $P^\mu=(...
- 151
5
votes
1
answer
219
views
How is Lorentz invariance of $S$-matrix related to vanishing of Hamiltonian density commutator at spacelike separations?
In Section 5.1 of the book, 'Quantum Theory of fields Vol-1' by Steven Weinberg, he says that if the Hamiltonian density commutes with itself at spacelike separation then the $S$-Matrix satisfies ...
- 195
1
vote
0
answers
133
views
If the scattering amplitudes are Lorentz scalars, why is S-matrix Lorentz covariant?
All observers should agree on the probabilities: $\mathcal{P}(\mathcal{R}_1 \rightarrow \mathcal{R}_2)$ in an inertial frame $\mathcal{O}$ = $\mathcal{P}(\mathcal{R}_1' \rightarrow \mathcal{R}_2')$ ...
- 433
2
votes
2
answers
419
views
Usefulness of $| {\rm in}\rangle$ and $| {\rm out}\rangle$ states in S-matrix description of QFT
I am currently reading Niklas Beisert's lecture notes on QFT, Chapter 10, on the scattering matrix $S$.$^1$ My main confusion lies in the construction of $\vert \rm in \rangle$ and $\vert \rm out \...
- 1,215
4
votes
1
answer
185
views
Weinberg's Coleman-Mandula theorem proof sufficient condition for isomorphism?
In Weinberg's QFT Volume 3 book on Supersymmetry, he presents his own proof of the Coleman-Mandula theorem. As part of the proof, he proves that the only possible internal symmetry generators must ...
- 3,514
3
votes
1
answer
600
views
Confusion over assumptions made in the LSZ reduction formula
I've been reading through a derivation of the LSZ reduction formula (http://www2.ph.ed.ac.uk/~egardi/MQFT_2013/, lecture 2, pages 2-3) and I'm slightly confused about the arguments made about the ...
- 3,207
2
votes
1
answer
949
views
Scattering Amplitude Not Invariant under Little Group?
I am trying to make sense of scattering amplitude recently. In some literature people say that if some number of massless particles collide together, one can theoretically express the scattering ...
- 261
2
votes
3
answers
2k
views
Derivation of the full generator of the Lorentz transformations
Let us study the subgroup of the Poincare group that leaves the point $x=0$ invariant, that is the Lorentz group. The action of an infinitesimal Lorentz transformation on a field $\Phi(0)$ is $L_{\mu \...
- 3,569
6
votes
1
answer
1k
views
S-operator lorentz invariance
How to show that $\hat {S}$-operator must be lorentz-invariant operator?
$$
|\Psi (t)\rangle = \hat {S} | \Psi (0) \rangle , \quad \hat {S} = \hat {T}e^{-i\int \hat {H}_{I}d^{4}x}.
$$
I have read ...
- 6,564