**Hitoshi Kitada** (*hitoshi@kitada.com*)

*Fri, 8 Oct 1999 02:17:15 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 904] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"**Previous message:**Lancelot Fletcher: "[time 902] IBM TeX plugin"**Next in thread:**Matti Pitkanen: "[time 904] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"

Dear Matti,

Matti Pitkanen <matpitka@pcu.helsinki.fi> wrote:

Subject: [time 901] Re: [time 899] Virasoro

conditions,renormalizationgroupinvariance,unitarity,cohomology

*>
*

*>
*

*> On Fri, 8 Oct 1999, Hitoshi Kitada wrote:
*

*>
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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)

*> > vanishes. As I reread your [time 894], I found it is interesting idea but
*

does

*> > 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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My point is that this formula uses your decomposition X=XP+X(1-P), but this

does not seem to give

<m_0|P|n_1>+<m_1|P|n_0>=0.

*>
*

*>
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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

*> > need to use cancellation.
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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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*>
*

Best wishes,

Hitoshi

**Next message:**Matti Pitkanen: "[time 904] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"**Previous message:**Lancelot Fletcher: "[time 902] IBM TeX plugin"**Next in thread:**Matti Pitkanen: "[time 904] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"

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