Physics & Math: Beyond Calculus for Subatomic Particles

[Gear300]

The mathematical aspects of calculus prove useful to physics to some extent. But I heard that once you start studying subatomic particles and quantum, calculus becomes somewhat inefficient at modeling the phenomenon. Just out of curiousity, what other higher level mathematics are being developed beyond the calculus?

 

[Mindscrape]

I don't think this belongs in the HW section, but further into everything, like in quantum, partial differential equations are important, as are special functions like Bessels, Hermite, Legendre, etc. Matrix methods and linear algebra are also very important. But you will never know how to do any of it if you aren't well founded in calculus, especially vector calculus.

 

[Gear300]

I see...seems logical. However, I also heard of some unfamiliar names for different types of mathematics...dont quite remember the names

 

[belliott4488]

Well, Group Theory becomes important in Particle Physics, and if you want to get deep into Gauge Field Theory, you get into Differential Geometry, Topology, and other kinds of advanced geometry.

 

[Gear300]

Interesting...I did hear that several of these new methods fell under those categories. I have one more question...is there a mathematical field currently being worked on that can be considered a branch of its own, similar to how Calculus became a new field in math?

 

[Mindscrape]

Constantly. I myself don't know much about it, but I believe the work with elliptic and modular forms was relatively recent. This would be a better question for the math forum. Generally, in physics you typically don't work on the cutting edge of math, though certain theories, such as string theory, are exceptions. I might argue that physicists know a broader range of math though.

 

[Gear300]

I would agree. I actually asked this question in this part of the forum because I'm thinking physicists would be more capable of answering this question than mathematicians: I'm still a student at physics and mathematics so I wouldn't know so much on this matter, but it seems as though some of the newer phenomenon in physics are somewhat leaping ahead of our current mathematics. Am I right or wrong?