- #1
Jimmy Snyder
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Homework Statement
On page 44 of Ryder's QFT, near the bottom of the page, it says:
Ryder said:it is straightforward to show, by writing out all four components of (2.94), that the eigenvalues of E are:
[tex]E = +(m^2 + p^2)^{1/2}[/tex] twice,
[tex]E = -(m^2 + p^2)^{1/2}[/tex] twice,
Homework Equations
Equation (2.94) is
[tex](\gamma^{\mu}p_{\mu} - m)\psi(p) = 0[/tex]
The Attempt at a Solution
Writing out all four components, and then taking the determinant and setting to zero, I get:
[tex]m^4 - (E^2 - p^2)^2 = 0[/tex] or [tex]m^4 = (E^2 - p^2)^2[/tex]
Taking the square root once:
[tex]\pm m^2 = E^2 - p^2[/tex] or [tex]E^2 = p^2 \pm m^2[/tex].
And taking the square root again:
[tex]E = \pm(p^2 \pm m^2)^{1/2}[/tex]
and I end up with different eigenvalues than I am supposed to.
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