 Quote by strangerep
Could you please give me a specific reference where these statements are derived rigorously?
(Or are they easy to derive but I'm still missing something?)
|
Oh, they're certainly not easy to derive. The fact that Wick products give densely defined operators was first proved by Jaffe in 1966 [1]. However I personally fined a later derivation by Segal in 1967 to be much clearer [2]. Segal has a very erudite way of writing, which you will either love or find very difficult to read.
I should also say the theorem is much harder to prove in the Hamiltonian approach that I'm discussing. In the Functional-Integral (Path-Integral) approach it's just a matter of evaluating a single Feynman diagram. See Glimm and Jaffe's book Section 8.5, Proposition 8.5.1.
[1] Jaffe, A. : Wick polynomials at a fixed time.
J. Math. Phys. 7, 1250 — 1255
[2] Segal, I. "Notes toward the construction of nonlinear relativistic quantum
fields, I. The Hamiltonian in two space-time dimensions as the generator
of a C*-automorphism group."
Proc. Natl. Acad. Sci. U. S. 57, p.1178—1183
|
[Edit: I sense a note of frustration in your post #241, so I just like to say two things:
a) THANK YOU for going to the effort in those earlier posts, and THANK YOU in advance
for (hopefully) future episodes of the climbing-the-ladder saga.
b) I do want to understand these things rigorously, including how one goes about
proving convergence since (among other things) acquiring such functional-analytic
skill is clearly valuable in any other non-Wightman approach that one might wish to
investigate.
|
You're more than welcome, I will be glad to continue the series of posts.