If the electro- magnetic field is that of a light quantum, the vacuum polarization eSects are equivalent to ascribing a proper mass to the photon. Previous calculations have yielded non-vanishing, diver- gent expressions for the light quantum proper mass. However, the latter quantity must be zero in a proper gauge invariant theory. The failure to obtain this result from a gauge in- variant formulation can be ascribed only to a faulty application of the theory, rather than to an essential deficiency thereof. When the e1ectro- magnetic field is that of a given current dis- tribution, one obtains a logarithmically divergent contribution to the vacuum polarization current which is everywhere proportional to the given distribution. This divergent result expresses the possibility, according to present theory, of creat- ing electron-positron pairs with unlimited energy, a situation that presumably will be corrected in a more satisfactory theory. Thus the physically significant divergence arising from the vacuum polarization phenomenon occurs in a factor that alters the strength of all charges, a uniform renormalization that has no observable conse- quences other than the conHict with the empirical finiteness of charge. The interaction between the electromagnetic field vacuum Ructuations and an electron, or more exactly, the electron-positron matter field, modifies the properties of the matter field and produces the self-energy of an electron. The mechanism here under discussion is commonly described as the virtual emission and absorption of a light quantum by an otherwise free electron, although an equally important effect is the partial suppression, via the exclusion principle, of the coupled vacuum Huctuations of the e1ec- tromagnetic and matter fields. In a Lorentz invariant theory, self-energy e6'ects for a free electron can only result in the addition of an electromagnetic proper mass to the electron's mechanical proper mass. Calculations performed for a stationary electron' have yielded a loga- rithmically divergent electromagnetic proper mass, a divergence that results from the possi- bility of emitting light quanta with unlimited energy. It is here, as in the vacuum polarization problem, that modifications will be introduced in a more satisfactory theory. However, the electromagnetic proper mass merely produces a renormalization of the electron mass that has no observable consequences, other than the conflict with the empirical finiteness of mass. It is evident that these two phenomena are quite analogous and essentially describe the interaction of each held with the vacuum fluctuations of the other field. The effect of these Auctuation interactions is simply to alter the fundamental constants e and m, although by logarithmically divergent factors.
You've reached the end of your free preview.
Want to read all 23 pages?