- #1
h-mina
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Hi, all
I'm reading peskin by myself.
I can't understand from eq(3.50) to eq(3.53).
i) What should I interpret [itex]\sqrt{p\cdot\sigma}[/itex]?
I guess below, but I can't understand [itex]\sqrt{\;\;}[/itex] of matrices.
\begin{eqnarray}
p\cdot\sigma=E \left(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right) - p^3\left(\begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array}\right) \\
= \left(\begin{array}{cc} E-p^3 & 0 \\ 0 & E+p^3 \end{array}\right)
\end{eqnarray}
And why is it the same as (3.49)?
ii)How can I confirm (3.50) is a solution of the Dirac equation?
iii)What's meaning of "large boost" in (3.52) and (3.53)?
If I understand the Dirac spinor more, is it easy transform?
When so, where can I study Dirac spinor easily?
Thanks in advance!
I'm reading peskin by myself.
I can't understand from eq(3.50) to eq(3.53).
i) What should I interpret [itex]\sqrt{p\cdot\sigma}[/itex]?
I guess below, but I can't understand [itex]\sqrt{\;\;}[/itex] of matrices.
\begin{eqnarray}
p\cdot\sigma=E \left(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right) - p^3\left(\begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array}\right) \\
= \left(\begin{array}{cc} E-p^3 & 0 \\ 0 & E+p^3 \end{array}\right)
\end{eqnarray}
And why is it the same as (3.49)?
ii)How can I confirm (3.50) is a solution of the Dirac equation?
iii)What's meaning of "large boost" in (3.52) and (3.53)?
If I understand the Dirac spinor more, is it easy transform?
When so, where can I study Dirac spinor easily?
Thanks in advance!
Last edited: