# [time 920] Re: [time 919] Re: [time 914] Re: [time 909] About your proof of unitarity

Sat, 9 Oct 1999 16:59:14 +0900

Dear Matti,
----- Original Message -----
From: Matti Pitkanen <matpitka@pcu.helsinki.fi>
Sent: Saturday, October 09, 1999 2:25 PM
Subject: [time 919] Re: [time 914] Re: [time 909] About your proof of
unitarity

>
>
> 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

I am speaking of general context without such a condition. If the limit above
exists, then it follows from it the unitarity.

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.
>
> Best,
> MP
>
>

Best wishes,
Hitoshi

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