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

*Thu, 7 Oct 1999 05:20:49 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 888] Re: [time 886] Unitarity finally understood!"**Previous message:**Matti Pitkanen: "[time 886] Unitarity finally understood!"**Next in thread:**Matti Pitkanen: "[time 888] Re: [time 886] Unitarity finally understood!"

Dear Matti,

I am still stumbling on the first step of your proof in "1. The condition

guarateing unitarity." Could you explain proof of this section step by step

without omitting any steps?

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

Subject: [time 886] Unitarity finally understood!

*>
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*>
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*>
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*>
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*> Dear Hitoshi,
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*>
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*> I believe that I understand the unitarity condition now.
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*> To streamline the notation I just denote
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*>
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*> L_0(int)==V ,
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*>
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*> and
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*>
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*> L_0(free)==L_0.
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*>
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*> |m>= |m_0> +|m_1>
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*>
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*> is the decomposition of scattering state to free or bare state
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*> and genuine scattering contribution (cloud of virtual particles.
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*>
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*> S=1+T
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*> ******************************************************
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*>
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*>
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*> 1. The condition guarateing unitarity
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*>
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*> The condition guaranteing unitarity is
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*>
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*> V|m>=V|m_0>
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Is this the only assumption in proving unitarity? Could you explain proof so

that a blind mathematician can understand it?

*>
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*> The action of interaction operator to dressed
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*> state is same as to bare state. The contribution
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*> of virtual cloud of particles to interaction vertex
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*> vanishes.
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*>
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*> Vanishing coupling constant and wave function renormalization
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*> are immediate consequences. This is just what is
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*> expected on basis of quantum criticality.
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*> Kahler coupling strength is fixed point of coupling constant
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*> evolution and since it is the fundamental coupling, all
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*> vertices are RG invariant.
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*>
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*> p-Adic coupling constant evolution means that Kahler coupling depends
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*> on p-adic prime labelling configuration space sectors
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*> so that continuous coupling constant evolution
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*> is effectively replaced by a discrete one.
*

Best wishes,

Hitoshi

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