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Light Cone Distribuitions

  1. Aug 20, 2012 #1

    I have been reading the excellent review by Eric Poisson, Ian Vega and Adam Pound:http://relativity.livingreviews.org/Articles/lrr-2011-7/fulltext.html [Broken]

    In section 12, Eq.12.15, there's something that I don't quite understand. They write:


    so they define the light cone Dirac Functionals [itex]\delta_{\pm}[/itex] with the functional [itex]\delta (\sigma)[/itex]. But they don't define [itex]\delta (\sigma)[/itex]. I suppose they intend to define a Dirac distribution along the unique geodesic that links two points in space time, but the Synge world function is defined for space,time and null geodesics, how is [itex]\delta (\sigma)[/itex] only restricted to the light cone?

    (You might also want to look in section 13.2 where they generalize for curved spacetime)

    Thank you and sorry if it's a silly question.
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Aug 20, 2012 #2

    George Jones

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    [itex]\delta (\sigma)[/itex] is not restricted to the light-cone, the support of [itex]\delta (\sigma)[/itex] is restricted to the light-cone. The support of a function is the closure of the set on which the function is non-zero.
  4. Aug 20, 2012 #3
    Oh, yes, that makes more sense.

    Altough, to clarify, if I have a base point [itex]x_1[/itex] and another point, say, [itex]x_2 \in I^+(x_1)[/itex], how would one see [itex]\delta(\sigma)[/itex] as a function of [itex]x_2[/itex]?

    I don't understand the argument of [itex]\delta[/itex], what should I visualize? [itex]x_3:=\sigma(x_1,x_2)[/itex] it's a scalar, what does it mean [itex]\delta(x_3)[/itex]?

    Sorry if i'm being annoying. Thank you.
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