kvblake2003

In Bjorken and Drell - QED part 1 I read a statement that one doesnt
use a square rooted Hamiltonian (H= SQRT/m*2.c*4+m*2.p*2/) in a wave
equation of the Schoedinger type
(–ih.dpsi/dt=H.psi) because after expanding the root in Taylor series
one gets all powers to infinity of the space derivatives. This makes
the theory non-local.

1.Now I don't inderstand how the n+1 derivative is more non- local
than the n-th derivative – in the end all is taken to the limit of the
local point)
2.Then in the quantum theory based on Schroedinger equation there are
only second order derivatives over space but nevertheless one is left
at the end with a non-local theory (EPR type paradoxes).

bruce scott tok

|> In Bjorken and Drell - QED part 1 I read a statement that one doesnt
|> use a square rooted Hamiltonian (H= SQRT/m*2.c*4+m*2.p*2/) in a wave
|> equation of the Schoedinger type
|> (–ih.dpsi/dt=H.psi) because after expanding the root in Taylor series
|> one gets all powers to infinity of the space derivatives. This makes
|> the theory non-local.
|>
|> 1.Now I don't inderstand how the n+1 derivative is more non- local
|> than the n-th derivative – in the end all is taken to the limit of the
|> local point)

It is not n+1 versus n but N_large versus n = 1 here. Think of finite
differences. With n = 1 you communicate with neighboring grid points.
With n = 1 applied N times you communicate with grid points a count N
away. Now let N --> \infty.
|> 2.Then in the quantum theory based on Schroedinger equation there are
|> only second order derivatives over space but nevertheless one is left
|> at the end with a non-local theory (EPR type paradoxes).

Here, think about elliptic equations.

--
cu,
Bruce

drift wave turbulence: http://www.rzg.mpg.de/~bds/

tadchem

Personally I would suggest a transformation of coordinate systems to
something in which your square root is a little more well-behaved,
possibly a rotation with renormalization.


Tom Davidson
Richmond, VA