Recent content by cgoakley

Yes, of course if you put free fields into the scattering calculations, you will get trivial results. That is not what he does. The interacting electron field contains, in higher order, a (free) electron combined with a (free) photon, an electron combined with an electron-positron pair and so...

If you are saying this, then with respect, I do not think that you have understood the approach at all. The steps are these: 1. Build a free field relativistic quantum field theory We are not going to argue about this - or are we? The Hamiltonian and other Poincare generators are...

Spacelike (anti)commutativity is not guaranteed, unless one introduces higher-order terms, certainly. What this has to do with causality is not so clear, though, as defining what one means by this in the quantum world is a lot harder than in the classical world. This I absolutely do not get...

The power series is obtained by expanding the QED equations of motion. If one simply defines one's theory such that the interacting fields are the free fields plus these leading terms then everything will be perfectly finite and rigorous, and the simple scattering amplitudes will be correctly...

I hope so, as this constructive QFT seems not to be able to generate cross-sections in 3+1 dimensions. We seem not even to be able to agree about the basic rules of logic. Stückelberg's covariant P.T. uses free field theory as its framework. You agree that free theory is rigorous. Yet you say...

Eugene, I do not understand your question. As you point out, what you have written down is just a definition.

Where was I trying to evade Haag's theorem? As I said, the interacting c/a operators in Stückelberg's covariant perturbation theory cannot be unitarily transformed to the non-interacting ones, even though they live in the same Fock space. This is consistent with Haag's theorem. A matrix...

Yes they are. You are making the additional assumption that if U(t) does not exist then free and interacting theories cannot live in the same Fock space. If you look at Källén's work you will see that interacting creation/annihilation operators are formed as sums of tensor products of free c/a...

"Haag's theorem only says that the Fock space created from the free vacuum by the free creation operators does not support an interacting theory." Incorrect. Haag's theorem says that the Fock space created from the free vacuum by the free creation operators is not unitarily equivalent to an...

I doubt very much that, to tree level at least, there is anything seriously wrong with the standard model. The problem is loops, which mostly diverge. HEP theorists have a gourmet's appreciation of different kinds of divergent integral, classifying them as "log", "quadratic", "quartic", etc...

Hi Sunset, What you are pointing out is that infinity minus infinity is completely indeterminate. Since it is completely indeterminate, the arbitrary function that you talk about could even depend on variables that never even entered the equations in the first place. What Zee, and the other...