1
vote
0answers
41 views

Conflict between Lippmann–Schwinger equation and Gell-Mann and Low theorem about energy

Lippmann–Schwinger equation states that scattering state will have the same energy as free state, while Gell-Mann Low theorem says that they have different enery. Lippmann–Schwinger equation says: ...
1
vote
1answer
52 views

$\mathrm{d} \Omega_{CM}$ for a $1\rightarrow 2$ particle decay?

The differential solid angle is described in e.g. Srednicki's QFT text but only for the case of scattering. Because in the case of scattering it's defined with respect to the incoming three-momentum ...
4
votes
1answer
80 views

Allowed interactions in bosonic string theory

In a quantum field theory, only a finite set of interactions are allowed, determined by the Lagrangian of the theory which specifies the interaction vertex Feynman rules. In string theory, an ...
1
vote
0answers
56 views

Scattering theory of Dirac equation in curved space-time in presence of a strong magnetic field

What is the exact solution of the Dirac equation in curved space-time in the presence of a strong magnetic field? The solution should be in momentum space for simplicity to calculate scattering cross ...
4
votes
0answers
55 views

Is it necessary to use decay width calculated at the same order as the scattering process?

I would like to calculate higher order corrections to a process for which there is an intermediate resonance which subsequently decays into lighter states. I am confused about how to treat the width ...
2
votes
0answers
38 views

Conversion of QCD cross section formula

I'm writing a program to calculate NLO cross sections for semi-inclusive high-$p_T$ pion production in proton-proton-collisions for my bachelor thesis. I've got a paper describing the production ...
8
votes
1answer
167 views

There are two definitions of S operator (or S matrix) in quantum field theory. Are they equivalent?

I read several textbooks of QFT and found that there are two kinds of definition of $S$ operator (or S matrix). First kind: Define $\hat{S}$ is map from out space to in space ...
2
votes
1answer
61 views

Materials about S-matrix and S-matrix theory

What is the best book or paper to learn about analytical structures of S-matrix and S-matrix theory? I already know books as The Analytic S-matrix by RJ Eden, PV Landshoff, DI Olive, JC P and Quantum ...
2
votes
1answer
87 views

What's the relation or difference between Lippmann-Schwinger equation and Dyson equation?

In quantum scattering theory, Green's Function is defined as [1] $$G_0(z)=(z-H_0)^{-1},$$ $$G(z)=(z-H)^{-1},$$ where $H_0$ and $H=H_0+V$ are separately non-interacting and interacting Hamiltonian. $V$ ...
0
votes
1answer
97 views

Little confusion in drawing Feynmam diagram

If the arrows of both the outgoing solid lines of the Feynman diagram corresponding to the bhabha scattering of $e^+$ and $e^-$, are just reversed, will it not describe same thing? Doesn't both imply ...
4
votes
0answers
88 views

Can $\langle\Omega|f|\Omega \rangle$ always be reduced to $\langle0|f|0\rangle$?

I've not come across any expression involving $\langle\Omega|f|\Omega\rangle$ in Srednicki's QFT book (please correct me if these exist there). On the other hand, they are abound in Chapter 7 of ...
5
votes
1answer
228 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 ...
1
vote
1answer
73 views

What do they mean with: photon scattering with $q^2=-Q^2\leq 0$

In a scattering problem, let q denote the four-momentum of the photon. Is $q^2=-Q^2\leq 0$ simply a statement of what metric one uses and simultaneously a definition of $Q^2$?
2
votes
3answers
224 views

Naive question about the S-matrix

In quantum field theory, the elements of the S-matrix are defined as the amplitude describing the transition from an initial $n$-particle state (the "in" state) to an final $m$-particle state: ...
4
votes
0answers
123 views

Calculating Forces via Feynman diagrams?

How would one go about calculating forces that test objects feel using Feynman diagram methods? For example, say we have a massive object in GR so that the metric takes on the standard ...
0
votes
0answers
44 views

What is the importance of the Odderon?

From hep-ph/0001149v1: (1) an Odderon contribution is absolutely necessary to reproduce quantitatively well the data; while its presence is not explicitly needed at $t = 0$, its inclusion is ...
4
votes
4answers
210 views

Is forward scattering = no scattering?

What is forward scattering? If it is equivalent to no scattering, then why not call it "no scattering"?
3
votes
1answer
203 views

Connected and strongly connected Feynman diagrams

Recently I read, that only connected Feynman diagrams give contribution of nonzero values into the scattering amplitude. Why it is so and what is the physical sense of connected diagrams (due to ...
15
votes
2answers
455 views

Why Cronin Effect Happens?

I'm looking for explanation on Cronin effect but unfortunately there's no Wikipedia entry or self-contained paper to start from. The statement of this effect is that: "At leading order, multiple ...
2
votes
0answers
76 views

Partial waves and the velocity expansion of a scattering cross section

I'm confused about the relation between the velocity expansion of a scattering cross section and the angular momentum (partial wave) expansion. For example, for dark matter annihilation, we write ...
4
votes
2answers
108 views

What is the sense of introducing generating functional to the summands of expansion of S-matrix?

Let's have generating functional $Z(J)$: $$ Z(J) = \langle 0|\hat {T}e^{i \int d^{4}x (L_{Int}(\varphi (x)) + J(x) \varphi (x))}|0 \rangle , \qquad (1) $$ where $J(x)$ is the functional argument ...
1
vote
0answers
57 views

Some strange transformation [closed]

In a lecture (look at the chapter "The fermion determinant in a constant field", p. 5) I found some strange transformation, which is given by eq. 18. How to prove it? Exactly, I don't understand the ...
6
votes
1answer
120 views

Importance of MHV amplitudes

Why are MHV amplitudes so important? How/where are they used and why do people keep trying to rederive them in many different ways?
2
votes
0answers
74 views

Møller scattering: twisted?

I am studying the Møller scattering, but I don't know how to get the twisted diagram from the S-matrix. Has anybody a good explanation?
5
votes
1answer
295 views

Scattering amplitude and LSZ formula

I'm arriving at a contradiction. To calculate the scattering amplitude, one usually follows the prescription given by the Feynman rules that you only consider fully connected diagrams with the ...
2
votes
1answer
169 views

Virtual particles and S-matrix

One of methods of introducing of virtual particles is using perturbation theory. We say that scattering matrice amplitude $M_{in \to out}$ contains of $\delta(P_{out} - P_{in})$, which realizes ...
2
votes
1answer
103 views

Why multiply by volume when integrating over final momenta in scattering amplitude calculations?

I am learning about calculating decay rates from quantum field theory amplitudes from David Tong's lecture notes (page 74 in the notes, 24 in document). However, I have some doubts: When he says the ...
11
votes
2answers
260 views

Locality in the scattering amplitude

Early in this talk by Nima Arkani-Hamed, he describes what locality means for scattering amplitudes. "Locality tells you that the only poles in the scattering amplitude occur when the sum of a subset ...
4
votes
0answers
861 views

How does one actually compute the amplituhedron?

I was watching Nima's very popular talk (download if you're using chrome) (also mirrored at youtube here) about the "Amplituhedron", which has suddenly become very popular recently. He talks all ...
3
votes
1answer
126 views

Divergence of One and Two Graviton Exchanges

At the bottom of pg. 3, Kiritsis states the following To appreciate the difficulties with the quantization of Einstein gravity, we look at a single-graviton exchange between two particles (Fig. ...
3
votes
1answer
272 views

Evaluation of QED amplitude with 1 external photon

I'm trying to compute the exact QED amplitude with one external photon. Suppose that the photon has 4-momentum $q$ and polarization $\varepsilon^\mu$. Peskin and Schroeder (p318) claim that ignoring ...
1
vote
0answers
480 views

Scattering Amplitude in second Born Approximation for the Yukawa potential

Does anyone know where I can find the analytical expressions of the scattering amplitude in second Born Approximation for the Yukawa potential? I need it for the both cases of the method of partial ...
5
votes
1answer
205 views

Charge Renormalization and Photon Propagator

I'm trying to understand charge renormalization in QED. I know that one can write the full photon propagator as $$\frac{-i\eta_{\mu\nu}}{q^2(1-\Pi(q^2))}$$ where $\Pi$ is regular at $0$. Obviously ...
4
votes
1answer
259 views

What is the formal definition of spin-independent vs. spin-dependent scattering?

In the search for WIMPs as the dark matter particle, there is an important distinction between spin-independent and spin-dependent scattering. Roughly, WIMPs scattering from nucleons through a ...
4
votes
1answer
158 views

Quantum field theory meson scattering calculation (scalar yukawa theory)

Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson ...
6
votes
1answer
200 views

Setting of renormalization scale in field theory calculations

In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
8
votes
1answer
133 views

Significance of Poles of Correlation Function in QFT

In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
4
votes
1answer
302 views

A question from Weinberg QFT

I'm self-studying Weinberg QFT. I'm confused by his treatment of scattering theory . I have the following question: He introduces the free particle states $\Phi_{\alpha}$ but I'm not sure what is ...
2
votes
1answer
181 views

Alternative methods to derive the static potential in the NR limit of QED

In QED, one can relate the two-particle scattering amplitude to a static potential in the non-relativistic limit using the Born approximation. E.g. in Peskin and Schroeder pg. 125, the tree-level ...
6
votes
1answer
232 views

Database of scattering amplitudes

I want to check whether my result for the invariant amplitude of the electron-electron scattering (to lowest order in $\alpha$; t+u channels) is correct or not. I can't find any reference that has ...
5
votes
2answers
350 views

Can scattering amplitudes be simplified with 1PI diagrams?

I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
1
vote
1answer
235 views

Integral in Peskin and Schroeder

I'm having a bit of a slow day, and can't see how to do the following integral in Peskin and Schroeder (page 107 for anyone with the book). We've derived in the centre of mass frame the integral over ...
3
votes
1answer
382 views

Scattering Processes in Scalar Yukawa Theory

I'm trying to compute nucleon-nucleon scattering in scalar Yukawa theory. Here we view a nucleon as a complex scalar field $\psi$ and a meson as a real scalar field $\phi$. They interact through ...
3
votes
1answer
158 views

Inclusion of information about external particles to calculate scattering amplitudes

In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states $$ A = \int\limits_{\rm{life time}} d\tau ...
1
vote
1answer
505 views

Feynman Rules for massive vector boson interactions

I am stuck at the beginning of a problem where I am given an interaction term that modifies the regular QED Lagrangian. It involves the interaction between a photon field and a massive vector boson: ...
0
votes
1answer
153 views

Scattering Amplitudes in Centre of Mass Frame

I'm reviewing page 59 of the QFT notes here and am a little confused by a reference frame argument. You can compute the second order probability amplitude term for nucleon-nucleon scattering to be ...
3
votes
1answer
162 views

Is the Møller wave operators $\Omega_\pm$ related to $\lim_{t\rightarrow\infty}U(t)$ of field theory?

When we want to compute correlation functions $\langle\Omega|\,T\hat{\phi}(x_1)\ldots|\Omega\rangle$ in an interacting quantum field theory, we relate it to the free-field objects $|0\rangle$ and ...
2
votes
3answers
472 views

Scalar Field Redefinition and Scattering Amplitude

Consider a field redefinition $$ \phi \rightarrow \phi' = \phi+\lambda \phi^2 $$ Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result ...
9
votes
2answers
1k 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 ...
9
votes
1answer
456 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} ...