What is an object with a zero square?

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In summary, the conversation was about a type of object whose square is zero and its applications to quantum theory. It was described as having a similarity to complex numbers and possibly being related to dual numbers, superspace, and Grassmann numbers. It was also mentioned that it could refer to isotropic vectors with the property of x*x = 0. Further information can be found in post number 5 by Zinq and through research on isotropic vectors.
  • #1
ergospherical
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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"... :)
 
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  • #2
How about the Lie product? If you call the elements left-invariant vector fields then it even sounds like an object.
 
  • #3
ergospherical said:
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?
 
  • #4
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?
 
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Thank you, this looks like it
 

What is an object with a zero square?

An object with a zero square is an object that has a surface area of zero. This means that the object has no measurable length, width, or height, and therefore has no surface area.

What does it mean for an object to have a zero square?

Having a zero square means that the object has no surface area. This could be due to the object being infinitely small or having no measurable dimensions.

Can an object have a zero square?

Yes, an object can have a zero square. This typically occurs with theoretical or abstract objects that have no physical existence or have dimensions that are infinitely small.

What are some examples of objects with a zero square?

Some examples of objects with a zero square include a point in geometry, a singularity in astrophysics, and a theoretical object with no measurable dimensions.

Why is it important to understand objects with a zero square?

Understanding objects with a zero square is important in various fields of science, such as mathematics, physics, and engineering. It helps us to better understand theoretical concepts and phenomena that may not have a physical manifestation in our world.

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