# 2.9 Lightlike compactification, d

A First Course in String Theory

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Represent your answer to part (c) in a spacetime diagram. Show two points related by the identification (2) and the space and time axes for the Lorentz frame $S'$ in which the compactification is standard.

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Note 1:

The identifications $\displaystyle{ x \sim x + 0 }$ and $\displaystyle{ x \sim x + \infty }$ have the same meaning, which is that $x$ has no identification at all. In other words, there is NO non-zero real number $r$ such that

$\displaystyle{ x \sim x + r }$

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Note 2:

\displaystyle{ \begin{aligned} \begin{bmatrix} ct \\ x \\ \end{bmatrix} &\sim \begin{bmatrix} ct - 2 \pi R \\ x + 2 \pi \sqrt{R^2 + R_S^2} \\ \end{bmatrix} \end{aligned} }

This identification must be done to both the space and time coordinates. In other words, it cannot be done to only one of $ct$ and $x$.

— Me@2021-04-13 12:02:13 PM

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2021.04.14 Wednesday (c) All rights reserved by ACHK