Massless Particles from Massive Theory: Understanding the m->0 Limit

[muppet]

In Zee's textbook, the photon and "graviton" propagators are derived as the m->0 limit of massive spin 1,2 particles; this works for the photon, but not the graviton. Weinberg adds the caveat that we obtain electrodynamics from the massive theory only if we couple the particles to a conserved source. In Peskin and Schroeder, the Weyl equations are presented as the Dirac equation in the limit of vanishing mass, and as far as I know nothing goes wrong.

Are there any general rules as to when it is and is not possible to derive the physics of a massless particle from the massive case?

 

[Bill_K]

Zee: I think you're referring to the "2/3 anomaly"? Later on, pp 426-427, Zee gives the explanation for this paradox, namely that the limit m → 0 is not uniformly valid, and the discrepancy exists only beyond a characteristic distance scale which becomes indefinitely large as m → 0.

Weinberg: The comment about coupling to a conserved source holds for both electromagnetism and gravity. In the case of electromagnetism the source is J^μ while for gravity it's T^μν, both of which are conserved.

Dirac/Weyl: The difference is that the Dirac equation has both right-handed and left-handed solutions. If you take the limit m → 0 you'll wind up with a right-handed Weyl particle and a left-handed one also.