Suppose I have a Feynman Diagram with a closed fermion loop. This introduces a negative sign, and a trace over the product of the propagators.
Is the same Feynman diagram, but with the arrows in the loop going in the opposite direction, a distinct diagram? In other words, are there really two diagrams, which we can take into account by introducing a factor of 2?
If the answer to the above is “yes,” then does this also apply to ghost diagrams?