What is Scattering amplitudes: Definition and 21 Discussions
In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationarystate scattering process.The latter is described by the wavefunction
ψ
(
r
)
=
e
i
k
z
+
f
(
θ
)
e
i
k
r
r
,
{\displaystyle \psi (\mathbf {r} )=e^{ikz}+f(\theta ){\frac {e^{ikr}}{r}}\;,}
where
r
≡
(
x
,
y
,
z
)
{\displaystyle \mathbf {r} \equiv (x,y,z)}
is the position vector;
r
≡

r

{\displaystyle r\equiv \mathbf {r} }
;
e
i
k
z
{\displaystyle e^{ikz}}
is the incoming plane wave with the wavenumber k along the z axis;
e
i
k
r
/
r
{\displaystyle e^{ikr}/r}
is the outgoing spherical wave; θ is the scattering angle; and
f
(
θ
)
{\displaystyle f(\theta )}
is the scattering amplitude. The dimension of the scattering amplitude is length.
The scattering amplitude is a probability amplitude; the differential crosssection as a function of scattering angle is given as its modulus squared,
Physicist Nima ArkaniHamed has taken an approach to understand fundamental physics based on geometry (specifically, positive geometry). This started with his work with Jaroslav Trnka in the amplituhedron [1] and later it was generalised to the associahedron [2],the EFThedron [3]...
I was...
Looking to calculate the amplitude and cross section of the process: electron + positron to photon + Z boson.
Basically the annihilation resulting in Z + gamma rather than gamma +gamma.
My question is mainly about how to deal with the polarization states with the Z boson, since there are 3 and...
I know $$ i\mathcal{M}(\vec {k_1}\vec{k_2}\rightarrow \vec{p_1}\vec{p_2})(2\pi)^4\delta^{(4)}(p_1 +p_2k_1k_2) $$ =sum of all (all connected and amputated Feynman diagrams), but what is meant by 1 loop order? In other words, when I take the scattering matix element...
Hi!
In QFT we are usually interested in actions that are hermitian. Say we are looking at scattering of Dirac fermions with a real coupling constant g, whose Lagrangian is given by:
$$L= \bar{\psi}(i \gamma_{\mu} \partial^{\mu} m) \psi  \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi ...
The term which is relevant for the calculus is:
$$ \bar u(p) \gamma^\alpha \frac{1}{\displaystyle{\not}p+\not k} \gamma^\nu \frac{1}{\displaystyle{\not}p'\not k} \gamma^\beta v(p') \frac{k_\alpha k_\beta}{k^2} $$
$$ \bar u(p) \displaystyle{\not}k \frac{1}{\displaystyle{\not}p+\not k}...
Hey there! I've recently been looking at calculating amplitudes, densities of states and scattering cross sections in QFT, but am having a little bit of trouble with the exact form of the cross section  particularly with factors of ##2E## for the energies of the incoming and outgoing particles...
Homework Statement
Given an interaction Lagrangian $$ \mathcal{L}_{int} = \lambda \phi \bar{\psi} \gamma^5 \psi,$$ where ##\psi## are Dirac spinors, and ##\phi## is a bosonic pseudoscalar, I've been asked to find the second order scattering amplitude for ##\psi\psi \to \psi\psi## scattering...
I have an expression
##\mathcal{Im}[RT^*e^{2ip}]=T^2\sin p ##, where ##R=Ae^{ip}+Be^{ip} ## and ##p ## is a real number.
This ultimately should lead to ##\mathcal{Im}[A+B+Te^{2ip}]=0 ## upto a sign (perhaps if I didn't do a mistake).
There is a condition on ##R ## that it is real...
Is A_pp(s,t)=A_pBARp(t,s) true based on crossing symmetry?
Consider pp and pBARp elastic colissions (p + p > p + p and p + BAR(p) > p + BAR(p)). The scattering amplitudes are related by crossing in the following way:
1) A_pp(s,t)=A_pBARp(u,t) \simeq A_pBARp(st,t) (energy large compared to...
I am reading Griffiths' Introduction to Quantum Mechanics, specifically the chapter on scattering. He is discussing the scenario where an incoming beam of particles scatter off an azimuthally symmetric target.
At large separation ##r## from the scattering centre, the wavefunction for incoming...
Hi.
My question is about nucleonnucleon scattering.
In David Tong's lecture note, he discusses Wick's theorem and nucleon scattering (page 5860).
My problem is that I don't know how to calculate the second line of eq(3.48):
\begin{equation}
<p'_1, p'_2:\psi^\dagger (x_1) \psi (x_1)...
Homework Statement
Consider two real scalar fields \phi,\psi with masses m and \mu respectively interacting via the Hamiltonian \mathcal{H}_{\mathrm{int}}(x)=\dfrac{\lambda}{4}\phi^2(x)\psi^2(x).
Using the definition of the Smatrix and Wick's contraction find the O(\lambda) contribution to...
I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short  two pages  so I find it instructive to post the pages here:
The point is that the author is doing this derivation...
I have tried to solve a scattering problem of two particles in one dimension, following the T operator theory, after to write the system in the center of mass reference. I have used the square potential
\begin{equation}
U(x) = \left\{ {\begin{array}{cc}
U_0 & 0 < x < a \\ 0 & \rm{Otherwise}...
Hi everyone, with this thread I kindly seek for advice from more experienced people to hear as many opinions as possible. I will try to explain the situation clearly:
I am doing a 4 years Msci programme in Theoretical Physics, in which I almost completed the third year. During the third year...
In quantum mechanics, we can define the scattering amplitude f_k(\theta) for two particles as the coefficients of an outgoing spherical wave. More precisely, the asymptotic behaviour (when r\rightarrow\infty) of a wave function of two scattering particles, interacting with some short range...
Homework Statement
Homework EquationsThe Attempt at a Solution
I've started from writing out the amplitude. Here I know that fermion has definite helicity so I can't sum over spins but I should input explicit forms of spinors. Am I correct? How to do this?
I would be grateful for helping me...
Hi. Do you know any book/paper/lecture notes where I can find complete derivation of Feynman rules for both scalar and pseudoscalar Yukawa theory, and maybe an example of application to decay of fermion?
Homework Statement
I'm working with the Yukawa theory, where the interaction term in the Lagrangian density is g\varphi\overline{\psi}\psi. As an exercise for getting used to using the Feynman rules for the theory, I'm asked to show explicitly (i.e. I'm not allowed to invoke charge...
I have a very trivial question to ask and it would be great if someone could
help me in this.
The statement that '3point amplitudes' and the location of poles are sufficient to
determine any npoint amplitude at tree level is confusing to me. Don't I also need to know
4point amlitudes, for...
What Does "Quantum Gravity Scattering Amplitudes" Mean?
I've seen it referenced in a few papers but I can't seem to find a definition.
I know what "scattering amplitudes" means but don't understand the relationship with quantum gravity.
What precisely is doing the scattering in quantum gravity?