All Questions
Tagged with quantum-field-theory s-matrix-theory
100
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
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
5
votes
2
answers
1k
views
The use of $a^\dagger(\mathbf{k}) = -i \int d^3x e^{ikx}\stackrel{\leftrightarrow}{\partial}_0 \phi(x)$ in the derivation of the LSZ-formula
I noticed that in Srednicki's derivation of the LSZ-formula the expression (chapter 5) for the creation (and also later for the annihilation) operator by the field operator:
$$a^\dagger(\mathbf{k}) = -...
- 9,778
13
votes
2
answers
3k
views
Physical meaning of partition function in QFT
When we have the generating functional $Z$ for a scalar field
\begin{equation}
Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\left[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\right]},
\end{...
- 1,336
3
votes
1
answer
708
views
Scalar derivative couplings: Effects on S-matrix and Feynman Rules
In Schwartz's field theory book ch. 7.4.2 he claims that interaction Lagrangians like
$${\cal L}_{\rm int} = \lambda \phi_1(\partial_{\mu}\phi_2)(\partial_{\mu}\phi_3)\tag{7.101}$$
lead to the Feynman ...
- 447
14
votes
2
answers
2k
views
Why does the action have to be hermitian?
The hermiticity of operators of observables, e.g. the Hamiltonian, in QM is usually justified by saying that the eigenvalues must be real valued.
I know that the Lagrangian is just a Legendre ...
- 243
10
votes
4
answers
615
views
Why can we shift the field $\phi$, so that $\langle \Omega | \phi(x) | \Omega \rangle = 0$?
Problem
Introduction
In different derivations of the LSZ reduction formula the author makes a shift of the field $\phi(x)$
$$
\phi'(x) = \phi(x) - \langle \Omega | \phi(x) | \Omega \rangle,
$$
and ...
- 199
9
votes
4
answers
2k
views
Different kinds of S-matrices?
It seems to me that the notion of an "S-matrix" refers to several different objects
One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
Squark
7
votes
3
answers
1k
views
Time-ordered operator in Srednicki
On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order ...
- 5,569
4
votes
1
answer
1k
views
Regarding a small step in the derivation of the LSZ formula
I'd like to prove the LSZ formula, but there is a specific step that is bugging me a lot. I know there are many subtleties in its derivation, but I'm not worrying about this right now: I'm trying to ...
3
votes
1
answer
600
views
Confusion over assumptions made in the LSZ reduction formula
I've been reading through a derivation of the LSZ reduction formula (http://www2.ph.ed.ac.uk/~egardi/MQFT_2013/, lecture 2, pages 2-3) and I'm slightly confused about the arguments made about the ...
- 3,207
21
votes
1
answer
5k
views
Unitary quantum field theory
What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one ...
- 415
16
votes
1
answer
4k
views
When we define the S-matrix, what are "in" and "out" states?
I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with
$$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle
=
S^{-1}
\...
- 163
12
votes
1
answer
3k
views
Free Vacuum vs Interacting Vacuum and Wick's theorem
I'm studying perturbation theory in QFT and I stumbled on a conceptual problem.
My understanding of the interplay between LSZ reduction formula and the Gell-Mann & Low perturbation series is that:...
- 497