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

*Thu, 7 Oct 1999 19:26:29 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Lancelot Fletcher: "[time 902] IBM TeX plugin"**Previous message:**Hitoshi Kitada: "[time 900] Re: [time 899] Virasoro conditions,renormalization groupinvariance,unitarity,cohomology"**In reply to:**Matti Pitkanen: "[time 899] Virasoro conditions,renormalization group invariance,unitarity,cohomology"**Next in thread:**Hitoshi Kitada: "[time 903] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"

On Fri, 8 Oct 1999, Hitoshi Kitada wrote:

*> Dear Matti,
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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 (19)
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*> vanishes. As I reread your [time 894], I found it is interesting idea but does
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*> not seem to work. I calculated like a blind mathematician:
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*>
*

*> m_1=Ym_0, Y=\sum_{k>0}(-X)^k =X(1+Y),
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*>
*

You srat from state |m_1> and manipulate it.

*> (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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OK

*>
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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.

*> = 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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This is state |m_1> as far as I can understand and should not vanish.

*> If this does vanish, your T is 0, not only that sum T+T^dagger=0: One would
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*> need to use cancellation.
*

I must admit that I cannot follow what you mean. You demonstrate that

|m_1> can be written as |m_1> = (1-Z)^(-1)X|m_0>

OK?

Certainly, if T is zero if |m_1> vanishes. But why |m_1> should vanish?

If your argument shows that |m_1> vanishes then I am in trouble

but your argument seems to show that |m_1> does NOT vanish??

It seems that I do not understand your point!

Best,

MP

**Next message:**Lancelot Fletcher: "[time 902] IBM TeX plugin"**Previous message:**Hitoshi Kitada: "[time 900] Re: [time 899] Virasoro conditions,renormalization groupinvariance,unitarity,cohomology"**In reply to:**Matti Pitkanen: "[time 899] Virasoro conditions,renormalization group invariance,unitarity,cohomology"**Next in thread:**Hitoshi Kitada: "[time 903] Re: [time 901] Re: [time 899] Virasoro conditions,renormalizationgroupinvariance,unitarity,cohomology"

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