# What are the uses of quaternions in Physics?

• C.E
In summary, the conversation discusses the use of quaternions in physics, specifically in mechanics and classical yang-mills SU(2) gauge theories. The speaker also mentions 'geometric algebra' as an extension of the concept of imaginary numbers and suggests looking at resources in the computer graphics literature for further information on quaternions. However, they also caution against spending too much time on this topic without a proper education and guidance.

#### C.E

Hi, I really want to learn about the applications of quaternions in Physics (I have posted in this section as apparently they can be used a lot in Mechanics). Anyway I was wondering if anyone knew of any good books (Undergraduate level),websites or interesting facts about this topic.

I don't know much about them but I heard that they are used to express rotations. you might want to look at this:
http://modelingnts.la.asu.edu/

the above link is about 'geometric algebra' which is, like quaternions, an extension of the concept of imaginary numbers which involves the idea of rotations. but it seems to be broader and possibly more useful than quaternions (as you can see from the links on that page)

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I have never seen quaternions in mathematical classical mechanics books (Arnold, Abraham) but I would be interested if anyone knows of a quaternionic discussion along these lines.

It goes a little beyond the undergraduate level, but quarternions are the natural way to express instanton solutions in classical yang-mills SU(2) gauge theories (which are like a more advanced version of Maxwell's equations) cf Atiyah 1979.

I just want to comment that 'geometric algebra' is not a mainstream topic, and that personally I regret the time I've wasted on these kinds of things during my education. Until the math dept offers a class on geometric algebra, I don't recommend bothering with it.

You might try looking at the computer graphics literature. Quaternions are used in video games.

## What are Quarternians in Physics?

Quarternians in Physics are a type of mathematical entity known as quaternions. They were first discovered in the 19th century and have since been used in various areas of physics, such as quantum mechanics and electromagnetism.

## How are Quarternians different from other mathematical entities?

Unlike real numbers, which are represented on a one-dimensional number line, quaternions are represented on a four-dimensional space. They also have different properties and rules for operations compared to other mathematical entities.

## What are some applications of Quarternians in Physics?

Quarternians have been used in various areas of physics, such as in quantum mechanics to describe spin states of particles, in electromagnetism to describe magnetic fields, and in general relativity to describe rotations in four-dimensional space and time.

## What are the challenges in using Quarternians in Physics?

One of the main challenges in using Quarternians in Physics is their non-commutative property, which means that the order of operations matters. This can be difficult to work with and understand, compared to other mathematical entities with commutative properties.

## Are Quarternians still relevant in modern physics?

Yes, Quarternians are still relevant in modern physics and have been used in recent advancements, such as in the study of quantum entanglement and in the development of quantum computers. They also continue to be a topic of research in areas such as string theory and supersymmetry.