I recently started learning feynman diagrams but I am a bit confused by how they are constructed from scratch (we are expected to memorize them without knowing exactly how they work). In particular, how do you know which gauge boson a particular particle interaction has, and which direction to draw this boson travelling? (I can usually figure out the particles using conservation laws but for the bosons I don't have any similar device.)
Thanks
Which gauge boson? Any one that couples to the charges the particle carries, and of course depending on the process (or interaction) you want do describe. So if you want to describe em interactions it will be a photon, if you want do describe $\beta$-decay it will be a $W$-boson (here conservation laws help you again: know the process must be a weak interaction as the flavour is changed and it cannot be a $Z$ as then conservation of charge would be broken).
A gauge boson line has no direction (!), as the direction indicated in a Feynman diagram does (usually) not indicate the momentum or travel direction, but the flow of the fermion number (therefore if the direction goes into the vertex it is an anti-particle)! The direction of the momentum can be fixed independently and arbitrarily (as long as momentum conservation at each vertex is guaranteed).
Often it is not emphasized enough, that only the topological structure of the Feynman diagram is relevant (that is, any time-axis in the diagrams is just for making it easy to read, it has no physical significance!).
Bottom line: The way Feynman diagrams are introduced in introductory courses on particle physics is considered harmful! Furthermore, some details are not handled uniformly in all fields of physics using Feynman diagrams (or different books in one field).
How Feynman diagrams are properly introduced? Feynman diagrams are diagrammatic, one-to-one representations of terms in the perturbation series. This can be found in any text book on QFT, but it is not quite simple (and requires a firm grasp of quantum mechanics to understand).
The Feynman rules for a given theory are actually derivable in quantum field theory, and are not specified ad-hoc. Typically, you can just read off the interaction rules from your Lagrangian. For example, in QED the Lagrangian contains a term $$A_\mu j^\mu$$ where $$j^\mu = ie\bar\Psi\gamma^\mu\Psi$$ is the conserved current.
Since this term has at least 3 fields, we can consider it an interaction and just read off the rule for this type of interaction as $$ie\gamma^\mu.$$ Things get a bit trickier when derivatives show up in the couplings.
This is a bit of cheat, as you really have to go through the full steps of deriving the Feynman rules, but know at least that they are derivable. When in doubt, you can look up the Feynman rules for our big theories out there, but if you end up using them often enough you'll remember the important ones.
