How prevalent is geometric algebra/calculus?

[Mike706]

Hello,

I am working through Clifford Algebra to Geometric Calculus, and supplementing with Hestenes' other books, as well as Geometric Algebra for Physicists.

I'm not looking for advice on the books or learning materials (feel free to chime in if you have an opinion on the matter, though!). I am just curious how common it is to see geometric algebra/calculus in current mainstream physics research. I'm really enjoying the subject, but I want to know if it is a small niche or widespread. Speculation on future trends of the subject's prevalence would also be appreciated.

I want to make sure I shouldn't be focusing my efforts elsewhere.

Thanks for your help,
Mike

 

[chiro]

Hey Mike706.

This might interest you:

http://www.mrao.cam.ac.uk/~clifford/pages/introduction.htm

 

[Muphrid]

I've not really seen it explicitly brought up in a mainstream context. I think there are a lot o fpossibilities for it, as it can be said to underlie all the stuff we do in 2d (complex analysis), 3d, and 3+1d spaces, and the insight it provides in unifying all the disparate descriptions of these is really powerful, but I don't think it's really "caught on" yet.

 

[brombo]

Applications of Geometric Algebra

Outside of Cambridge geometric algebra has mainly caught on for computer vision and robotics (in adopting something new engineers are usually ahead of physicists).

In physicis the main application is the gauge theory of gravity (Cambridge). The problem in physics is that academic physicists are under such pressure to publish or perish that they cannot take the time to learn a new mathmatical formalism when they already know formalisms that can solve the problems they have even though the new formalism could greatly simplify the solutions.

In order for geometric algebra/calculus to enter the physics mainstream it need to be taught in the undergraduate math ciriculum. If you are interested I have extensive notes (based on Doran and Lasenby) and symbolic GA software (python) at

https://github.com/brombo/GA

 

[homeomorphic]

Clifford Algebras make an appearance in the Dirac equation (and generally with spinors, which are all over the place in particle physics). But I suppose it's too tangential for a lot of physicists to study in depth.