Matti Pitkanen (matpitka@pcu.helsinki.fi)
Thu, 4 Nov 1999 09:11:05 +0200 (EET)
On Wed, 3 Nov 1999, Stephen P. King wrote:
> Dear Matti,
>
> I am reading and thinking hard about the implications of this idea! I
> am very interested in the relationship that you see between
> supersymmetry and the algebraic identity. I have a couple of questions:
> 1) Are the p-adic number fields well-orderable, e.g. can we define a
> unique > or < relation between pairs of p-adic numbers within the p-adic
> number fields?
No. This is reflected as ultrametricity, which
corresponds mathematically to spin glass property and is one of the
strongest motovations for introducing p-adicization.
> 2) Are the p-adic number fields themselves well-orderable?
You probable mean that one could say that there is ordering
with respect to p in some sense? One can say that the larger
the value of p is, the more refined the p-adic topology is.
Best,
MP
> Later,
>
> Stephen
>
>
> Matti Pitkanen wrote:
> >
> > Dear Stephen and all,
> >
> > I have worked with the sharpened form of Riemann hypothesis
> > stating that the phase factors p^(iy) are Pythagorean
> > (complex rational) phases for all primes p when y corresponds
> > to zero z=1/2+iy of Riemann zeta.
> >
> > The sharpened hypothesis allows various interpretations: for instance,
> > the matrix elements of the time development operator
> > U(t) for arithmetic quantum field theories are
> > Pythagorean phases when *time t is quantized* such
> > that z=1/2+it corresponds to zero of Riemann zeta!
> >
> > For these values of time time development operator
> > of arithmetic QFT would allow p-adicization by
> > phase preserving canonical identification.
> >
> > I attach the tex file.
> >
> > Best,
> > MP
> >
> > ------------------------------------------------------------------------
> > Name: sRiemann.tex
> > sRiemann.tex Type: IBM techexplorer TeX files (APPLICATION/x-tex)
> > Encoding: BASE64
>
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