Feynman diagram calculation tool
![feynman diagram calculation tool feynman diagram calculation tool](https://www.secretsofuniverse.in/wp-content/uploads/2020/04/annihilation-diagram-Feynman-positron-electron-antimuon-formation.jpg)
Relativistic Dirac equation had one big problem and that was negative energies. The time-ordered product (T) can be expressed in the form of a normal ordered product( represent on-shell particles) and Feynman green’s functions ( represent off-shell particles) using Wick’s theorem. Now, in perturbation theory, this can be expanded and we get : Now, scattering amplitudes for physical processes can be found using the S matrix given by: where H I is the interaction Hamiltonian density That is why off-shell particles are also called virtual particles. But the photon in the above diagram does not follow this, instead, the RHS can take any value so that the energy and momentum are conserved at the vertices. For example, photons that are on the shell follow. Here the off-shell represents particles that do not have a fixed mass. The lighter curvy line is an off-shell photon that conserves overall energy and momentum at the two vertices. Thus they are on-shell particles that are solutions to respective field equations. The dark external lines represent incoming and outgoing electrons. The above diagram is the simplest tree for electron scattering.
![feynman diagram calculation tool feynman diagram calculation tool](https://feyncalc.github.io/Images/hand.png)
Before this, let’s see a simple tree-level Feynman diagram, These diagrams have simplified a lot of lengthy calculations and prove to be very helpful.īut why do Feynman diagrams work? How does it give correct results? The answer to these can be found in Wick’s theorem. Feynman diagrams have been a very effective tool in scattering amplitude calculations of perturbative quantum field theory.