**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Thu, 7 Oct 1999 20:26:09 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Lancelot Fletcher: "[time 905] IBM TeX plugin"**Previous message:**Hitoshi Kitada: "[time 903] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"**In reply to:**Matti Pitkanen: "[time 901] Re: [time 899] Virasoro conditions,renormalization groupinvariance,unitarity,cohomology"

On Fri, 8 Oct 1999, Hitoshi Kitada wrote:

*> Dear Matti,
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*>
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*> Matti Pitkanen <matpitka@pcu.helsinki.fi> wrote:
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*>
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*> Subject: [time 901] Re: [time 899] Virasoro
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*> conditions,renormalizationgroupinvariance,unitarity,cohomology
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*>
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*>
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*> >
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*> >
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*> > On Fri, 8 Oct 1999, Hitoshi Kitada wrote:
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*> >
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*> > > Dear Matti,
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*> > >
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*> > > Thanks for posting your paper. I read it but before going to physical
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*> > > justification part I again stumbled on mathematical part: the proof that
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*> (19)
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*> > > vanishes. As I reread your [time 894], I found it is interesting idea but
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*> does
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*> > > not seem to work. I calculated like a blind mathematician:
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*> > >
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*> >
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*> >
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*> >
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*> > > m_1=Ym_0, Y=\sum_{k>0}(-X)^k =X(1+Y),
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*> > >
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*> >
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*> > You srat from state |m_1> and manipulate it.
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*> >
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*> >
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*> > > (BTW note (1+r)^{-1}=\sum_{k=or>0} (-r)^k not r^k !)
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*> > >
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*> > > = Xm_0 + Xm_1 (1)
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*> > >
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*> > > = Xm_0 + XPm_1 + X(1-P)m_1
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*> >
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*> > OK
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*> > >
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*> > > XPm_1 = 0 yields
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*> > >
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*> > > m_1 = Xm_0 + X(1-P)m_1
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*> > >
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*> > You are manipulating the state m_1 in the following. OK.
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*> >
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*> >
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*> > > = Xm_0 + Zm_1, Z=X(1-P),
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*> > >
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*> > > = Xm_0 + ZXm_0 + ZXm_1 (by (1))
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*> > >
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*> > > = (1+Z)Xm_0 + ZXPm_1 + ZX(1-P)m_1
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*> > >
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*> > > =(1+Z)Xm_0 + ZX(1-P)m_1 (by XPm_1=0)
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*> > >
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*> > > = ....
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*> > >
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*> > > = (1+Z+Z^2+Z^3+...)Xm_0 +lim_{k->infty}Z^kXm_1
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*> > >
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*> > > =(1-Z)^{-1}Xm_0 + lim_{k->infty}Z^kXm_1.
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*> > >
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*> > > This does not seem to vanish in general.
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*> > >
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*>
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*> My point is that this formula uses your decomposition X=XP+X(1-P), but this
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*> does not seem to give
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*>
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*> <m_0|P|n_1>+<m_1|P|n_0>=0.
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But as I see it, the last formula above is for |m_1>

rather than this quantity. Perhaps there is some mistyping

or confusion on my side.

Perhaps we should leave for a moment and look the consequences.

In particular, I would be happy for your comments concerning

the construction of the p-adic cohomology.

Best,

MP

*>
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*>
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*> >
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*> >
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*> > This is state |m_1> as far as I can understand and should not vanish.
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*> >
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*> >
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*> > > If this does vanish, your T is 0, not only that sum T+T^dagger=0: One
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*> would
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*> > > need to use cancellation.
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*> >
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*> > I must admit that I cannot follow what you mean. You demonstrate that
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*> >
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*> > |m_1> can be written as |m_1> = (1-Z)^(-1)X|m_0>
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*> > OK?
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*> >
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*> > Certainly, if T is zero if |m_1> vanishes. But why |m_1> should vanish?
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*> > If your argument shows that |m_1> vanishes then I am in trouble
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*> > but your argument seems to show that |m_1> does NOT vanish??
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*> > It seems that I do not understand your point!
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*> >
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*> > Best,
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*> > MP
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*> >
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*> >
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*>
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*>
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*> Best wishes,
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*> Hitoshi
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*>
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*>
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*>
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**Next message:**Lancelot Fletcher: "[time 905] IBM TeX plugin"**Previous message:**Hitoshi Kitada: "[time 903] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"**In reply to:**Matti Pitkanen: "[time 901] Re: [time 899] Virasoro conditions,renormalization groupinvariance,unitarity,cohomology"

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