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

*Sun, 3 Oct 1999 16:14:47 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 868] Re: [time 864] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847]Unitarity of S-matrix"**Previous message:**Hitoshi Kitada: "[time 866] Re: [time 864] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847]Unitarity of S-matrix"**In reply to:**Matti Pitkanen: "[time 864] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847] Unitarity of S-matrix"**Next in thread:**Matti Pitkanen: "[time 869] Re: [time 865] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847]Unitarity of S-matrix"

Dear Matti,

Your observation in the following is correct.

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

Subject: [time 865] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time

847]Unitarity of S-matrix

*>
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*>
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*>
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*> I noticed what might be the reason for the paradoxal conclusion
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*> about the triviality of S-matrix.
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*>
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*>
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*> The expression of S-matrix is
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*>
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*> <m_0|Sn> = <m_0| P*(1/(1+X)|n_0>
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*>
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*> Expand this to geometric series to get
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*>
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*> ...= delta (m,n) + sum_n <m_0| X^n|n_0>
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*>
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*> = delta (m,n) + (1/i*epsilon) sum_n <m_0| L_0(int) X^(n-1)|n_0>
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*>
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*> Here I have used X= (1/L_0(free)+iepsilon)L_0(int) to the first
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*> X in the expansion in powers of X.
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*>
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*> The point is that formula contains 1/epsilon factor!!
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*>
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*> Thus the limit is extremely delicate. S-matrix is notrivial
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*> if L_0(int)|m_0> is of order epsilon and goes to zero at
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*> the limit epsilon->0.
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*>
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*>
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*> This is dangerously delicate but I think that similar problems
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*> must be encountered with ordinary time dependent scattering theory
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*> when one restricts to 'energy shell' E=constant.
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Also in time dependent expression, taking the limit t -> \infty requires a

delicate argument and as well dangerous (;-)

*> The task would
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*> be to find proper formulation or possibly understand why p-adics
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*> save the situation.
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Before going to p-adics, there is a possibility to be checked: If standpoint

of real numbers works or not?

Best wishes,

Hitoshi

**Next message:**Matti Pitkanen: "[time 868] Re: [time 864] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847]Unitarity of S-matrix"**Previous message:**Hitoshi Kitada: "[time 866] Re: [time 864] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847]Unitarity of S-matrix"**In reply to:**Matti Pitkanen: "[time 864] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847] Unitarity of S-matrix"**Next in thread:**Matti Pitkanen: "[time 869] Re: [time 865] Re: [time 861] Re: [time 860] Re: [time 855] Re: [time 847]Unitarity of S-matrix"

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