All Questions
17
questions
0
votes
1
answer
52
views
Square of the Feynman amplitude for $a +b\to c+d$ and its reverse
In quantum field theory, if a process $a +b\to c+d$ is allowed by a certain interaction Lagrangian (hermitian), the reverse process, $c+d\to a+b$, must also be allowed (as far as I understand) by the ...
- 11.8k
2
votes
1
answer
65
views
Field redefinitions in the Higgs mechanism
Consider the Higg's mechanism for a simple $U(1)$ theory. Leaving aside the lagrangian which consists of a kinetic term for the gauge field, a covariant derivative term and the potential term for the ...
- 1,791
0
votes
1
answer
104
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What is a particle in the context of QFT with interactions?
This is a crossposting of the same question from mathoverflow: https://mathoverflow.net/q/454768/
It seems that this question was not received well there, claiming that this question is not ...
- 121
4
votes
0
answers
70
views
Redefinition of fields and interpretation of the particle content
Suppose I have some Lagrangian $\mathcal L_1$ involving multiple fields $\phi_i$ with interactions. I can reparametrize the Lagrangian in terms of new fields $\psi_i$ by inserting some ...
- 153
2
votes
2
answers
227
views
Polology of Feynman amplitudes, Section 10.2, Weinberg
In Weinberg's QFT Volume 1 section 10.2, we basically find that we have a pole when we have an intermediate particle state; the momentum of the intermediate state is on-shell. I am having trouble ...
- 433
1
vote
0
answers
147
views
LSZ reduction formula relation
LSZ formula gives a relation between the scattering amplitudes and correlators as
$$\langle f |i \rangle = (-i)^{m+n}\int \Pi_{i=1}^m d^4x_, e^{ik_i'x_i (\Box_{x_i} -m^2)}\Pi_{j=1}^n d^4x_, e^{ik_j ...
- 3,464
3
votes
0
answers
97
views
Adiabatic turn-on of free multi-particle states
Consider a second-quantized operator $\mathcal{H}_{full}$ describing some interacting QFT, whose action is known on a set of Fock states $\{\mathcal{|F\rangle}\}$, which, in turn, are the eigenstates ...
- 2,921
2
votes
0
answers
107
views
Energy Renormalization and Vacuum Diagrams
I have been reading the lecture notes of Coleman's course on QFT. When developing scattering theory with the use of a cutoff function, he mentions that, in order to ensure that the free vacuum ...
- 3,915
5
votes
1
answer
801
views
Trouble deriving expression for differential scattering cross section from $S$-matrix
I am following the derivation of the scattering cross-section from Peskin and Schroeder textbook. On page 105, we get an expression for the differential cross-section:
$$d\sigma = \left(\prod_f \frac{...
- 316
1
vote
1
answer
181
views
What is particle under potential in quantum field theory?
Let's say we solve the Schrodinger equation with infinite well. We can quantize the field by the resonance state and can get the annihilation and creation operator. So we will get the sort of particle ...
- 479
15
votes
2
answers
690
views
Why do we need to embed particles into fields?
In QFT we have the so-called embeding of particles into fields. This is discussed at full generality in Weinberg's book, chapter 5. In summary what one does is:
From Wigner's classification, for each ...
- 36.4k
9
votes
1
answer
1k
views
Is an interacting QFT Hilbert space a physical particles Fock space?
There are "Lectures on Quantum Field Theory" by P.A.M. Dirac, in which he claims that QFT state space is not a separable Hilbert space.
Also, I have seen some research papers (in axiomatic QFT), which ...
- 749
4
votes
1
answer
746
views
Status of particles in interacting QFT
From my readings in QFT and answers such as this, I've read that the concept of particles and particle-number in interacting systems becomes ill-defined in QFT.
Of course, in the real world, a number ...
- 385
3
votes
2
answers
2k
views
How to tell whether a Feynman diagram is $t$-channel or $s$-channel by looking?
By looking at a diagram, how does one tell whether it represents a $s$-channel process or a $t$-channel process i.e., without finding the amplitude? I'm familiar with Mandelstam variables but I've ...
- 26.8k
6
votes
1
answer
261
views
S-Matrix Interpretation and Predictions
How does one distinguish between the second-loop contribution of a known particle, and the first-loop contribution of a more massive-and as yet undiscovered-particle in the S-matrix and/or ...
- 321