# Relationship between lightlike and spatial compactification

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?

• What source are you reading from? – Physiks lover Jul 21 '13 at 19:03
• @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. – Dilaton Aug 1 '13 at 11:47
• @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. – Abhimanyu Pallavi Sudhir Aug 1 '13 at 12:24