Electromagnetism and Feynman diagrams

[Ray]

1. Feynman says all of electromagnetism follows from Maxwell equations.
2. Somebody (Pointing to a Feynman diagram of a photon/electron reaction) said all of electromagnetism is in that one diagram. So, can anyone help me with these two questions: how does point 1 come from point 2. And, how does a photon come from an EM field just by using it in a Langragian form?

 

[jostpuur]

I remember when I asked one particle physicists, that "how does Coulomb's force follow from that diagram?". The response was "no... we use these to calculate particle collision cross-sections". That's the unpleasant, but simple, truth You are not getting electromagnetism out of particle exchanges.

 

[astrokreng]

I can provide some clarification on the relationship between electromagnetism and Feynman diagrams.

First, let's address the statement that all of electromagnetism follows from Maxwell's equations. Maxwell's equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields, and how they are related to each other. These equations were developed by James Clerk Maxwell in the 19th century and are considered the cornerstone of classical electromagnetism.

On the other hand, Feynman diagrams are a graphical representation of mathematical equations that describe the interactions between particles in quantum field theory. These diagrams were developed by physicist Richard Feynman in the 20th century and have been used to successfully explain and predict many phenomena in particle physics.

So, while Maxwell's equations describe the behavior of classical electromagnetism, Feynman diagrams are used to describe the behavior of particles and their interactions at the quantum level. Therefore, it is incorrect to say that all of electromagnetism follows from Maxwell's equations alone. Feynman diagrams are necessary to fully understand and describe the behavior of particles in the electromagnetic field.

Now, let's address the second point about a photon coming from an electromagnetic (EM) field just by using it in a Lagrangian form. The Lagrangian is a mathematical function that describes the dynamics of a system in terms of its energy. In quantum field theory, the Lagrangian is used to describe the interactions between particles and fields.

In the case of an EM field, the Lagrangian describes the interactions between the photon (the particle that mediates the electromagnetic force) and the electron (the charged particle that creates the EM field). When this Lagrangian is used, it can be shown that the photon does indeed emerge from the EM field.

To summarize, Feynman diagrams are a powerful tool for understanding the behavior of particles in the electromagnetic field, but they are not the only factor in understanding electromagnetism. Maxwell's equations and the use of Lagrangians are also crucial in fully describing the complex interactions between particles and fields. I hope this helps to clarify the relationship between electromagnetism and Feynman diagrams.