Vladimir Krivchenkov - Perturbation Theory

Perturbation Theory

Quantum field theory is a generalization of quantum mechanics. Krivchenkov believed that people need to understand at least the non–relativistic theory. He almost asked students to excuse him for the field theory, where only perturbation theory can be offered. Not only do the perturbation theory series diverge, but each perturbational term also in some sense is infinite, and a special renormalization of the interaction constant is required to give the result the physical sense.

One of the colleagues of Krivchenkov, Yurii Shirokov tried to construct quantum field theory in terms of wave packets, without divergences, using the algebra of generalized functions, but even now this approach is not sufficiently developed. Krivchenkov told students that they are supposed to build up a "true" theory, not just a perturbation, that always gives a divergent series. This statement (dogma) applies not only to Field Theory and quantum mechanics, but to any perturbation theory with respect to any distributed system; the perturbation series always diverges. Krivchenkov had realized this and brought this knowledge to students. Many problems in his books stress this property of perturbation theory.