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Please use small words

  1. Nov 14, 2006 #1
    "Between the simplest rank 0 field theory and the simplest rank 2 field theory is the simplest rank 1 field theory."

    I found this quote buried in a huge thread. It seems to be the central point of that thread but I don't know what it means.

    Can someone explain what it means using really small words that will fit into my little brain?
     
  2. jcsd
  3. Nov 14, 2006 #2

    robphy

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    I think that these are references to ways to describe the gravitational field. A "rank 0" theory is a "scalar" theory, like ordinary Newtonian gravitation with the gravitational potential (a scalar field) [tex]\phi[/tex] [which satisfies the Poisson Equation [tex]\nabla^2\phi=\rho[/tex]]. A "rank 2" theory is a "tensor" theory, like the Einstein's General Relativity with a "rank 2" object, the metric tensor field [tex]g_{ab}[/tex], which must satisfy the Einstein Field Equations. A "rank 1" theory is a "vector" theory, like Maxwell's Electrodynamics with a vector potential [tex]A_a[/tex].

    From Quantum Field Theory, these ranks are associated with the "spin" of the [massless] quanta of that theory.

    I vaguely recall an argument from a Quantum Field Theory class that somehow rejects odd-spin theories for gravitation. (Does it have to do with the attractive property of gravity?)
     
  4. Nov 14, 2006 #3

    Claude Bile

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    The only time I have heard the "rank 0, rank 1.." terminology is wrt to Tensors, with a rank 0 tensor being a scalar, rank 1 being a vector and rank 2 being a matrix.

    I guess the statement is saying that vector field theory is harder than scalar field theory but easier than matrix field theory...which doesn't make a great deal of sense. Tensor fields of different ranks are all linked via their derivatives, i.e. the derivative of a scalar field is a vector field and so on.

    Perhaps whoever posted it meant that vector calculus lies in between scalar calculus and tensor calculus in difficulty....

    Without any context, I can't really add any more insight.

    Claude.
     
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