All Questions
Tagged with quantum-field-theory s-matrix-theory
463
questions
187
votes
2
answers
31k
views
Why do we not have spin greater than 2?
It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also ...
- 2,861
38
votes
4
answers
5k
views
Scattering, Perturbation and asymptotic states in LSZ reduction formula
I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
- 26.8k
26
votes
1
answer
531
views
Is the converse of Weinberg's statement on the cluster decomposition principle true?
In Weinberg's "The Quantum Theory of Fields, Vol. 1", Section 4.4, page 182, the author says:
We now ask, what sort of Hamiltonian will yield an $S$-matrix that satisfies the cluster ...
- 36.4k
22
votes
2
answers
6k
views
What is the physical interpretation of the S-matrix in QFT?
A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers.
Given a quantum field theory when ...
- 221
21
votes
2
answers
4k
views
Quantum Field Theory in position space instead of momentum space?
What are the reasons why we usually treat Quantum Field Theory in momentum space instead of position space? Are the computations (e.g. of Feynman diagrams) generally easier and are there other ...
- 1,783
21
votes
1
answer
5k
views
Unitary quantum field theory
What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one ...
- 415
20
votes
2
answers
4k
views
Equivalence Theorem of the S-Matrix
as far as I know the equivalence theorem states, that the S-matrix is invariant under reparametrization of the field, so to say if I have an action $S(\phi)$ the canonical change of variable $\phi \to ...
- 355
19
votes
1
answer
5k
views
Green's function in path integral approach (QFT)
After having studied canonical quantization and feeling (relatively) comfortable with it, I have now been studying the path integral approach. But I don't feel entirely comfortable with.
I have the ...
- 5,228
17
votes
2
answers
1k
views
What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?
For background, I'm primarily a mathematics student, studying geometric Langlands and related areas. I've recently been trying to catch up on the vast amount of physics knowledge I'm lacking, but I've ...
- 171
17
votes
2
answers
441
views
Quantum symmetries: $S$ or $Z$?
Let $I$ be the action of some QFT (gauge-fixed and including all the necessary counter-terms); $S$ the associated scattering-matrix; and $Z$ the partition function (in the form of, say, a path ...
17
votes
2
answers
685
views
Is there an analogue of the LSZ reduction formula in quantum mechanics?
In quantum field theory the LSZ reduction formula gives us a method of calculating S-matrix elements. In order to understand better scattering in QFT, I will study scattering in non-relativistic ...
- 1,045
16
votes
3
answers
11k
views
What actually means to compute things at tree level?
In his QFT book, Matthew Schwartz first talks about tree level as follows:
We will begin by going through carefully some of the predictions that the theory gets right without infinities. These are ...
- 36.4k
16
votes
1
answer
4k
views
When we define the S-matrix, what are "in" and "out" states?
I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with
$$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle
=
S^{-1}
\...
- 163
16
votes
2
answers
2k
views
CFT and the Coleman-Mandula Theorem
The Coleman-Mandula theorem states that under certain seemingly-mild assumptions on the properties of the S-matrix (roughly: one particle states are left invariant and the amplitudes are analytic in ...
- 161
15
votes
1
answer
2k
views
Does de Sitter space admit an asymptotic S-matrix?
From the Penrose diagram of de Sitter space, we see it has a future and past conformal boundary, and they are both spacelike. So, does de Sitter space admit an asymptotic S-matrix? Sure, in the usual ...
- 245