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Natural Science Forum / Physics / Particle Physics / March 2005a question about non-locality
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). |> 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 [quoted text clipped - 6 lines] |> 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.  Signaturecu, Bruce drift wave turbulence: http://www.rzg.mpg.de/~bds/ > |> 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 [quoted text clipped - 11 lines] > 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 |
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