My question concerns the 1/2 factor in the exponential of Eq. (3.49) of Peskin and Schroeder.(adsbygoogle = window.adsbygoogle || []).push({});

This equation concerns the Lorentz boost transformation of a spinor along the z-axis (or 3-direction).

According to Eq. (3.26):

[itex]S^{03} = -\frac{i}{2}\begin{bmatrix}\sigma^3 & 0 \\0 & -\sigma^3\end{bmatrix}[/itex]

and Eq. (3.30):

[itex]\Lambda_{1/2} = exp(-\frac{i}{2}\omega_{03} S^{03})[/itex]

Combining these two expressions and using the infinitesimal boost (according to Eq. (3.48) and Eq. (3.21)): [itex]\omega_{03} = \eta[/itex] (here [itex]\eta[/itex] is the rapidity):

[itex]\Lambda_{1/2} = exp(-\frac{1}{4}\eta \begin{bmatrix}\sigma^3 & 0 \\0 & -\sigma^3\end{bmatrix})[/itex]

My problem is that Peskin and Schroeder have a 1/2 factor where my simple substitution gives a 1/4!?!

Am I misinterpresting the meaning of [itex]\omega_{03}[/itex]? I am assuming that [itex]\eta = \beta[/itex] (v/c) from my understanding of Eq. (3.21)... this might be a problem?!?

Thanks for your help!

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# Factor in equation (3.49) of Peskin and Schroeder

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