Hi! I'm reading David Tong's notes on QFT and I'm now reading on the chapter on the dirac equation(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Imaginary eigenvalues of gamma matrices

**Physics Forums | Science Articles, Homework Help, Discussion**