The subtlety of Feynman rule lies simply as a copout clause of avoiding the singular energy poles. In the spirit of this holiday season, this similarly believes that Santa Claus lives everywhere else except at the North Pole or at the South Pole. On the other hand, Kris Kringle acting on true spirit of giving, certainly would avoid the poles since hardly anyone there, except of course, emperor penguins of Antarctica and hopefully a pioneering messenger named Happy Feet tapping humanity of thousands of years of harsh reliance on the depleting marine bounty.
In the spirit of great discovery, Feynman rules amounts to smarty pant’s theoretical hocus pocus avoiding the question: why zero mass exists? The few bosons with zero mass are photons, gluons, and gravitons. It is futile to hope of finding the last two groups by the usual standard conventional experiments. The massive ones are the weak vectors bosons: W+, W-, and Z0. Except for the neutrinos, all fermions have detectable mass. The ultimate ruler of mass is the scalar Higgs boson, which ever refuses to appear on stage for fear of having to donate more and more free mass to the needy masses. Like the Scrooge character of 1843 novel by Charles Dickens, the Higgs boson is up for education by the three ghosts of spacetime’s past, present, and future.
Feynman avoided the poles simply by giving the mass an infinitesimal negative imaginary part. Therefore, a complex mass is just a displaced complex circle whose center is not the origin of the complex plane. It calls for some serious complicated transformation procedures, which must be Lorentz invariant in order to agree with special relativity.


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