Feynman diagrams

1. Dec 9, 2015

Immortalis

I am trying to learn about Feynman diagrams and am confused by some of the notation. In particular, what do matrices, in particular the Dirac adjoint, have to do with Feynman propogators and why are they in imaginary terms?

2. Dec 9, 2015

samalkhaiat

Feynman diagrams are terms in the perturbative expansion of the scattering operator
$$S = \sum_{n = 0}^{\infty} \frac{(-i)^{n}}{n!} \int \cdots \int d^{4}x_{1} \cdots d^{4}x_{n} \ T \big\{ \mathcal{H}(x_{1}) \cdots \mathcal{H}_{I}(x_{n}) \big\} ,$$
where $T$ time-orders the product of operators, and $\mathcal{H}_{I}$ is the interaction Hamiltonian. For QED,
$$\mathcal{H}_{I}(x) = - \mathcal{L}_{int.}(x) = -e N \big\{ \bar{\psi}(x) \gamma^{\mu}\psi (x) A_{\mu}(x) \big\} ,$$ where $\mathcal{L}_{int.}$ is the interaction Lagrangian, and $N\{\cdots\}$ denotes the normal ordering product. For two scalar operators at $t_{1}\neq t_{2}$, Wick’s theorem relates the T-product to the Normal order product $N\{\cdots\}$ and the Feynman propagator $\Delta_{F}$:
$$T \big\{ \phi^{\dagger}(x_{1}) \phi (x_{2}) \big\} = N \big\{ \phi^{\dagger}(x_{1}) \phi (x_{2}) \big\} + i \Delta_{F}(x_{1}-x_{2}) ,$$ with
$$i \Delta_{F}(x_{1}-x_{2}) = \langle 0 | T \big\{ \phi^{\dagger}(x_{1}) \phi (x_{2}) \big\} | 0 \rangle .$$
Since you are learning about Feynman diagrams, make sure that you learn and understand all the under-lined words and phrases.

3. Dec 10, 2015

Immortalis

As I am currently a high school senior with basic experience in physics and calculus, and much of this terminology flies over my head, would you know any good places where I can break this down so I can understand it?

4. Dec 10, 2015

samalkhaiat

Well, calculations based on Feynman diagrams are post-grad stuff, normally covered in quantum field theory courses. So, you should for now just trust the descriptive explanation of the diagrams. I believe Frank Close wrote a nice little book about elementary particles and theire interaction, which can be appropraite to your level.

Last edited: Dec 10, 2015
5. Dec 10, 2015

sandy stone

I think Feynman himself touches on his diagrams towards the end of his book QED: the Strange Theory of Light and Matter. It's a pretty good introduction.