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Integral brane world

  1. Aug 24, 2011 #1
    if the extra coordinate [tex]y \in [-\pi,\pi] [/tex] with [tex] A(y)=A(y+2 \pi) [/tex] and [tex]A'[/tex] is non continuom in [tex] -\pi,0,\pi [/tex]

    why

    [tex] \oint (A'e^A)' dy =0 [/tex] but [tex] \oint e^A dy \neq 0 [/tex]????
     
  2. jcsd
  3. Aug 28, 2011 #2
    What is A?
     
  4. Aug 28, 2011 #3
    The first integral is a total derivative so

    [tex]\oint ( A' e^A)' dy= A'(\pi) e^{A(\pi)} - A'(-\pi) e^{A(-\pi)} [/tex]

    which would vanish provided

    [tex] A'(\pi) = A'(-\pi) [/tex]

    but you seem to imply this may not be the case????

    The integral
    [tex]\oint A' e^A dy= \oint ( e^A)' dy = e^{A(\pi)} - e^{A(-\pi)} =0 [/tex]

    is also a total derivative and certainly does vanish due to the boundary conditions.


    I see no reason for

    [tex] \oint ( e^A) dy [/tex]

    to vanish as its not a total derivative so it depends on the explicit form of the function [tex]A(y) [/tex].
     
  5. Sep 22, 2011 #4
    but [tex] A' [/tex] is discontinuous in [tex] -\pi,0,\pi [/tex]
     
  6. Sep 23, 2011 #5
    [tex]A=|y|[/tex]
    where
    [tex]A' = 1 , y \in )0,\pi( [/tex]

    [tex]A' = -1 , y \in )-\pi,0( [/tex]

    [tex]A ' = undefined , y =- \pi, 0,\pi [/tex]
     
    Last edited: Sep 23, 2011
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