Hitoshi Kitada (email@example.com)
Mon, 11 Oct 1999 15:36:41 +0900
Matti Pitkanen <firstname.lastname@example.org> wrote:
Subject: [time 933] Re: [time 931] Re: [time 928] Re: [time 923] Unitarity
> On Mon, 11 Oct 1999, Hitoshi Kitada wrote:
> > Dear Matti,
> > Matti Pitkanen <email@example.com>
> > Subject: [time 931] Re: [time 928] Re: [time 923] Unitarity
> > >
> > >
> > > Dear Hitoshi,
> > >
> > > Still one question, can you tell in five words(;-) what is the
> > > 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
> > the basic quantity. Standard approach uses state function. The
> > 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.
Yes. If one can formulate in Hamiltonian formalism in QFT, it would give a
similar structure to standard one, and one can argue in a similar way. There
is a possibility here, but Hamiltonian formalism would be possible only in
Euclidean metrics and usually it is not taken seriously. Of course there is a
method of introducing Euclidean metric by replacing i*t by a new real variable
x^0. My assertion is not in this Euclidetization, but in using genuine
Euclidean metric as the basic metric.
> 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.
In this respect, there is a possibility of applying standard method, but the
metric might be a problem.
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