Let x1, x2, x3 be the components of a complex vector.(adsbygoogle = window.adsbygoogle || []).push({});

If x1^2 + x2^2 + x3^2 = 0 Cartan calls this a isotropic vector.

So if,

x1 = a*exp(i*theta) then

x1^2 = a^2*exp(2*i*theta) ?

I think I'm being confused with what I read here,

http://www.sjsu.edu/faculty/watkins/spinor.htm

in particlular the definition of x*x = a^2 + b^2 + 2*i*ab

Thanks for any help.

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

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

# From Cartan's Theory of Spinors, x1^2 + x2^2 + x3^2 = 0

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