Regularization (physics) - Transport Theoretic Approach

Transport Theoretic Approach

According to Bjorken and Drell, it would make physical sense to sidestep ultraviolet divergences by using more detailed description than can be provided by differential field equations. And Feynman noted about a differential equations :“. . . for neutron diffusion it is only an approximation that is good when the distance over which we are looking is large compared with the mean free path. If we looked more closely, we would see individual neutrons running around.” And then he wondered, “Could it be that the real world consists of little X-ons which can be seen only at very tiny distances? And that in our measurements we are always observing on such a large scale that we can’t see these little X-ons, and that is why we get the differential equations? . . .Are they also correct only as a smoothed-out imitation of a really much more complicated microscopic world?”
Already in 1938, Heisenberg proposed that a quantum field theory can provide only an idealized, large-scale description of quantum dynamics, valid for distances larger than some fundamental length, expected also by Bjorken and Drell in 1965. Feynman's preceding remark provides a possible physical reason for its existence.