[time 919] Re: [time 914] Re: [time 909] About your proof of unitarity

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 9 Oct 1999 08:25:43 +0300 (EET DST)

On Sat, 9 Oct 1999, Hitoshi Kitada wrote:

> Dear Matti,
> I understand that you are talking in p-adic context, and as such the present
> proof does not harm your result.
> I do not want to disturb your satisfaction with your proof. Just I would like
> to conclude with a comment that the existence of the limit lim
> (1+R_0(z)V)^{-1} = lim R(z)(H_0-z) = lm (1-R(z)V): \HH_- -->\HH_- when Im z->0
> is the main issue, and if this is solved, the unitarity holds also in real
> case.

But if one has the condition VP|m_1>=0 S matrix is trivial in real
context since T^daggerT=0: this you certaily agree. The limits are
certainly delicate but as I said I must try to identify the architecture
of unitarity: the condition replacing the representability of S-matrix as
time development operator.

I hope that you understand that our starting points are different. You
have at your use refined scattering theory whereas I am desperately trying
to identify basic structural principles leading to "Feynmann rules".
Only after that functional analyst can come to my great building and
start decoration(-;). You certainly know that even quantum field theories
are still unkown territory for mathematicians (say functional integrals).
TGD generalize quantum field theories by replacing point like
particle with 3-surface: TGD is more interesting for mathematical dreamers
than "blind mathematicians" in its recent state.


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