- #26

strangerep

Science Advisor

- 3,153

- 968

Suppose we have a theorem which says "if A then B". We can't use it to[...]

In other words, [Haag's] theorem derives the non-existence of the interacting Hamiltonian from the covariant transformation law of the interacting field (1). In my formulation, I simply exchanged places of these two statements. I derived the non-existence of the covariant transformation law (1) from the existence of the interacting Hamiltonian [itex] H [/itex].

I think that both formulations are equivalent. [...]

automatically infer "if B then A". I.e: simply exchanging the places of

the two statements is not valid without supplying a detailed proof of the

reverse direction. It's like a maths exam question that asks the student

to prove "A if and only if B". If the student only proved the forward

direction "if A then B", but didn't also prove "if B then A", then

(s)he would not receive full marks.

That's why I said what you wrote is one approach for "evading"The reason why I chose to formulate Haag's theorem in the non-traditional form is that I have no reason to doubt the existence of interactions, however, I am very doubtful about the physical meaning and usefulness of "interacting fields". From this point of view, the theorem becomes completely harmless.

the theorem. I.e: if we don't like the consequences of a theorem, then we

must abandon one or more of its required pre-conditions. In your case,

you're advocating abandonment of the usual form of the boost transformation

law which had been phrased with a Minkowski spacetime picture in mind.

Personally, I think this is an interesting research direction to pursue, especially

in view of the well-known problems about Lorentz covariance of trajectories of

interacting particles discussed elsewhere.