What is an object with a zero square?

[ergospherical]

Earlier somebody was telling me about a type of object whose square is zero, and that apparently it has some applications to quantum theory (it wasn't explained very well...). Anyone know what he could have been talking about?

And no, it was not "0"... :)

 

[fresh_42]

How about the Lie product? If you call the elements left-invariant vector fields then it even sounds like an object.

 

[martinbn]

Earlier somebody was telling me about a type of object whose square is zero, and that apparently it has some applications to quantum theory (it wasn't explained very well...). Anyone know what he could have been talking about?

And no, it was not "0"... :)

That's way too vague. Can't you tell us a bit more what that someone told you?

 

[ergospherical]

Yeah, I mean there's quite a few things I can think of which have this property... e.g. nilpotent matrices of degree 2, null vectors, etc., but none of those apply

Can't remember any other useful details I'm afraid, apart from that they might have some similarity to complex numbers?

 

[martinbn]

Yeah, I mean there's quite a few things I can think of which have this property... e.g. nilpotent matrices of degree 2, null vectors, etc., but none of those apply

Can't remember any other useful details I'm afraid, apart from that they might have some similarity to complex numbers?

https://en.wikipedia.org/wiki/Dual_number

https://en.wikipedia.org/wiki/Dual_number#Superspace

https://en.wikipedia.org/wiki/Grassmann_number

 

[ergospherical]

Thank you, this looks like it

 

[Spinnor]

See post number 5 by Zinq and skip the garbage I wrote,

https://www.physicsforums.com/threads/shape-defined-by-x-c-3-and-x-x-0.860897/

Also see,

https://encyclopediaofmath.org/wiki/Isotropic_vector#:~:text=A non-zero vector that,x,x)=0.