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Hi! I'm reading David Tong's notes on QFT and I'm now reading on the chapter on the dirac equation

http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf

and I stumbled across a statement where he claims that

[tex] (\gamma^0)^2 = 1 \ \ \Rightarrow \text{real eigenvalues}[/tex]

while

[tex] (\gamma^i)^2 = -1 \ \ \Rightarrow \text{imaginary eigenvalues}.[/tex]

I'm a bit rusty on my linear algebra and just wondered why this is necessarily true. Why does the square of a matrix being positive and negative respectively mean real and imaginary eigenvalues?

http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf

and I stumbled across a statement where he claims that

[tex] (\gamma^0)^2 = 1 \ \ \Rightarrow \text{real eigenvalues}[/tex]

while

[tex] (\gamma^i)^2 = -1 \ \ \Rightarrow \text{imaginary eigenvalues}.[/tex]

I'm a bit rusty on my linear algebra and just wondered why this is necessarily true. Why does the square of a matrix being positive and negative respectively mean real and imaginary eigenvalues?

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