Matti Pitkanen (email@example.com)
Sat, 9 Oct 1999 20:07:18 +0300 (EET DST)
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(;-)!
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