[time 933] Re: [time 931] Re: [time 928] Re: [time 923] Unitarity

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Mon, 11 Oct 1999 09:18:40 +0300 (EET DST)

On Mon, 11 Oct 1999, Hitoshi Kitada wrote:

> Dear Matti,
> Matti Pitkanen <matpitka@pcu.helsinki.fi>
> Subject: [time 931] Re: [time 928] Re: [time 923] Unitarity
> >
> >
> > Dear Hitoshi,
> >
> > Still one question, can you tell in five words(;-) what is the difference
> > between QFT and wave mechanics approches? One might think that
> > basically there can be no difference if Hamiltonian quantization really
> > works. Didn't Schwinger follow the Hamiltonian quantization?
> >
> > MP
> My understanding is that QFT uses the operator-valued distribution which is
> the basic quantity. Standard approach uses state function. The formulations
> would be different in their interpretaion and applicability of standard
> scattering theory to QFT seems small.

The introduction of field operators is new element and Fock space replaces
the Hilbert space of wave functions. One can generalize
Lippmann-Scwinger to abstract Hilbert space and presumably does so.
You are right that the applicability at practical level is small.

In any case, in TGD configuration space spinor field is formally in
same position as classical Dirac spinor. No second quantization is
performed for it although spinor components correspond to
Fock states generated by second quantized induced spinor fields
on spacetime surfaces.


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