Bruce Scott TOK wrote:
Kevin Blake wrote:
|> 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.
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
.
