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

*Sat, 9 Oct 1999 20:07:18 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 926] Re: [time 913] Mind over Matter"**Previous message:**Matti Pitkanen: "[time 924] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"**In reply to:**Hitoshi Kitada: "[time 922] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"

Dear Hitoshi,

I think I understand now unitarity in rather satisfactory manner.

a) The proof of unitarity by

formal scattering theory fails because it uses scattering states

which contain off mass shell particles not satisfying free Virasoro

conditions. Free states and scattering states span different

state spaces. This is also the cause to the failure of

the the wave function renormalization to be trivial in quantum field

theories (formally it should be trivial).

b) In my proof of unitarity condition I explicitely use *on mass

shell projections of scattering states* so that the problems caused

by the nonequality of Hilb_0 and Hilb are not encountered! This

is quite an important advantage! In formal scattering theory

these projections are not used.

c) The condition VP|m_1>=0 explicitely guarantees that wave function

renormalization constants are trivial!

So it seems that my *deep* ignorance about scattering theory has

led me to the condition solving divergence problems and

forcing p-adics and leading to cohomology theory(;-)!

Best,

MP

**Next message:**Stephen P. King: "[time 926] Re: [time 913] Mind over Matter"**Previous message:**Matti Pitkanen: "[time 924] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"**In reply to:**Hitoshi Kitada: "[time 922] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"

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