Re: Dirac on renormalization (was: Is general relativity incompatible...)

Eugene Stefanovich wrote:

> Could you please tell me which of these three statements are not
> true?

> 3) Quantum theory with a deficient Hamiltonian (as in 1) and 2))
> cannot be considered complete. For example, in this theory,
> the spectrum of stationary states cannot be found by direct
> diagonalization of the Hamiltonian. The time evolution of
> non-stationary states cannot be described by the time evolution
> operator exp(iHt).

This one.

> The bright side is that Feynman-Dyson
> perturbation series for the S-matrix is finite
> (all infinities cancel out in each perturbation order)
> and accurate.

The same perturbation theory gives a series expansion, which is also
finite at each order, for all other quantities of interest. These
include the energy levels, states, dynamical quantities, etc. I know
that you will now ask for references. However, references were given
given many times along with explanations for how to use the information
provided in them. You'll just have to look for them in this group's
archives.

Igor

.