What is Feynman rules: Definition and 106 Discussions
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations which won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagrams, as would [Wilczek's] calculations that established a route to production and observation of the Higgs particle."Feynman used Ernst Stueckelberg's interpretation of the positron as if it were an electron moving backward in time. Thus, antiparticles are represented as moving backward along the time axis in Feynman diagrams.
The calculation of probability amplitudes in theoretical particle physics requires the use of rather large and complicated integrals over a large number of variables. Feynman diagrams can represent these integrals graphically.
A Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory. Within the canonical formulation of quantum field theory, a Feynman diagram represents a term in the Wick's expansion of the perturbative S-matrix. Alternatively, the path integral formulation of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to the final state, in terms of either particles or fields. The transition amplitude is then given as the matrix element of the S-matrix between the initial and the final states of the quantum system.
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I came across this difficulty comparing several versions of the Feynman rules for QED. I traced the problem back to a statement of Weinberg's in "The Quantum Theory of Fields (Vol 1)", Chapter 5, page 195. Weinberg is busy setting up for deriving free field...
Hi everyone,
In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions about his derivation.
1) As a first step, he rewrites the correlation function as
$$...
Several texts state the vertex HQET Feynman rule as : igTijvμ\frac{1}{1+\slashed{v}} with the reasoning for vμ presented as being due to the QCD interaction vertex being between two heavy quark propagators, which are \frac{1+\slashed{v}}{2v.k}, giving ...
Hi there. I'm trying to solve the problem mentioned above, the thing is I'm truly lost and I don't know how to start solving this problem. Sorry if I don't have a concrete attempt at a solution. How do I derive the Feynman rules for this Lagrangian? What I think happens is that in momentum...
To approach the problem I first studied section 1.3 and, more importantly, 1.4 of Osborn's notes.
We first need to compute ##\partial_j \omega_i (x)## and ##\omega_i (x)\omega_i (x)##
\begin{equation*}
\partial_j \omega_i (x) = \delta_{ij} + \underbrace{\partial_j (g_{ilm})}_{=0}x_l x_m +...
I am studying interacting scalar fields (from Osborn) using the path integral approach.
We define the functional integral \begin{equation*}
Z[J] := \int d[\phi] e^{iS[\phi] + i\int d^d x J(x) \phi(x)} \tag{1}
\end{equation*}
The idea is to differentiate ##Z[J]## with respect to ##J## and end...
Let us first take the S-matrix expansion (i.e. Dyson's formula)
\begin{align*}
S_{fi}&=\langle f | T \left\{ \exp\left( i\frac{\lambda_3}{3!}\int d^4 x :\phi \phi \phi (x) : + i\frac{\lambda_4}{4!}\int d^4 x :\phi \phi \phi \phi (x) : \right) \right\}| i \rangle \\
&= \langle f | i...
The weakly coupled theory is given by the Lagrange density$$\mathcal{L}=\mathcal{L}_0 + \mathcal{L}_I=\frac 1 2 \partial_{\mu} \phi \partial^{\mu} \phi - \frac{m^2}{2} \phi^2 - \frac{\lambda_3}{3!} \phi^3 - \frac{\lambda_4}{4!} \phi^4 \tag{1}$$
Where
\begin{equation*}
\mathcal{L}_0 = \frac...
In the following I will try to deduce the scattering amplitude for a specific interaction. My question is at the bottom, the entire rest is my reasoning to explain how I came to the results I present.
My working
Let's assume I would like to calculate the second order scattering amplitude in ##...
I'm working out the quark loop diagram and I've drawn it as follows:
where the greek letters are the Lorentz and Dirac indices for the gluon and quark respectively and the other letters are color indices.
For this diagram I've written...
For the diagram
In scalar field theory, I have obtained an integral which looks like
$$\int_{0}^{\Lambda} \frac{d^4 q}{(2\pi)^4} \frac{i}{q^2 - m^2 + i\varepsilon} \frac{i}{(p - q)^2 - m^2 + i\varepsilon}$$
I am required to calculate this and obtain the divergent amplitude
$$i\mathcal{M} =...
This is one of the problems I'm currently working on but understanding how to deduce the Feynman rules for this case would give me a better idea on how to do it for more general cases besides ##\phi^4## theory (which is the example commonly covered in books like Peskin and Greiner).
1. Homework...
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