Problem 2.1

A First Course in String Theory

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2.1 Exercises with units

Construct and evaluate a dimensionless number using the charge \displaystyle{e} of the electron (as defined in Gaussian system of units), \displaystyle{\hbar}, and \displaystyle{c}. (In Heaviside-Lorentz units, the Gaussian \displaystyle{e^2} is replaced by \displaystyle{\frac{e^2}{4 \pi}}.)

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\displaystyle{ \begin{aligned} \alpha &= \frac{e^2}{(4 \pi \varepsilon_0)\hbar c} \\ \alpha &= \frac{1}{137.035\,999\,679(94)} \\ \end{aligned} }

— Me@2010

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