The compactification of a spatial dimension, say $x^1$ given by the identification $x \sim x^1 + 2\pi R$ is said to be related to the lightlike compactification by a Lorentz boost :

$$ \left( \begin{array}{c} x^0 \\ x^1 \\ \end{array} \right) \sim \left( \begin{array}{c} x^0 \\ x^1 \\ \end{array} \right) +2\pi \left( \begin{array}{c} -R \\ R \\ \end{array} \right) $$

What exactly is the relationship between them? How can I see this? And what does it mean from a physics point of view?

  • $\begingroup$ What source are you reading from? $\endgroup$ Jul 21 '13 at 19:03
  • $\begingroup$ @Dimension10 yes, I have seen it thanks :-). Obviously such questions are not popular enough to get more votes (ambiguity of this sentence intented :-P ...). Yep it is mostly about the Lorentz transformations and the application of the issue in matrix/string theory is interesting too. $\endgroup$
    – Dilaton
    Aug 1 '13 at 11:47
  • 1
    $\begingroup$ @Dilaton: Uh... for all I know, the application in string theory is just getting Type IIA from M-theory compactified on a light - like circle . . . Don't know if there are other applications. $\endgroup$ Aug 1 '13 at 12:24

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