**Hitoshi Kitada** (*hitoshi@kitada.com*)

*Mon, 22 Mar 1999 23:41:03 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 47] Re: n-body dirac equation"**Previous message:**Stephen P. King: "[time 45] n-body dirac equation"**Next in thread:**Stephen P. King: "[time 47] Re: n-body dirac equation"

Dear Stephen,

Thanks for your information on n-body Dirac equation. I visited all pages, but

all seemed to be concerned with some NON-relativistic approximations.

I know Volker (Volker Enss, with whom I stayed at Caltech for almost 6 months

in 1985 or so and met also in Denmark and some other places). I have his

papers on inverse scattering on multi-dimensional scattering. His Hamiltonian

is also an approximation. One possibility is to choose Klein-Gordon equation,

but also in this case the invariance with respect to Lorentz or Poincare

transformation breaks down when one considers three or more body case. Also

there is an equation that seemed to have been abandoned at the discovery of

Dirac equation. The Hamiltonian of the equation is

H= \sqrt{p^2+m^2} + V(x),

where V(x) is the sum of pair potentials V_{ij}(x) over all pairs i, j of

particles. As V(x) is a potential describing action-at-a-distance, H is not

Lorentz invariant again. (I derived this type of equation as a Hamiltonian

describing actual observations in some of my papers (e.g. time_IV.tex).)

Volker's results cover this type of Hamiltonians.

To describe an exact N-body situation, it seems that we have to return to

Euclidean geometry if we want to retain quantum mechanics.

Best wishes,

Hitoshi

**Next message:**Stephen P. King: "[time 47] Re: n-body dirac equation"**Previous message:**Stephen P. King: "[time 45] n-body dirac equation"**Next in thread:**Stephen P. King: "[time 47] Re: n-body dirac equation"

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