Is Pure math of any use in Theoretical high energy physics?

[zahero_2007]

Is Pure math like functional analysis and real analysis of any use in Theoretical high energy physics research ? Do I need to learn them?

 

[zahero_2007]

Any one??

 

[lurflurf]

Functional analysis and real analysis are not (entirely) pure math, they are basic and highly applicable in application including but not limited to theoretical physics. The more important and harder to answer question is how a limed budget of time should be allocated to learning an unlimited amount of useful mathematics. My entirely unhelpful opinion is that between 3 and 30 percent of mathematics learning time should be devoted to functional analysis and real analysis depending on individual needs, abilities, and interest.

 

[homeomorphic]

I'm not in high energy, exactly, but I say learn what you are interested in. I don't know what level you are at. I think quantum mechanics provides nice motivation for functional analysis, so it's good to learn them together, or quantum mechanics first. Maybe functional first, if you are more mathematical, but I kind of look down on that, even though I am a mathematician (some PDE might also suffice in place of QM).

If your style is very mathematical, you can be like John Baez and know limitless amounts of math, but work in quantum gravity (although he quit that). If your style is more towards physics, I suspect you can probably get by if you almost ignore math, except whatever you need to learn along the way. So, it's really whatever you are interested in, I think.

 

[Matrix0]

Pure math, including functional analysis and real analysis, is an essential tool in theoretical high energy physics research. Theoretical physicists use mathematical models and equations to understand and predict the behavior of particles and systems at the highest energies, and pure math provides the necessary framework for these models.

Functional analysis, which studies the properties of functions and their transformations, is particularly useful in high energy physics because it allows for the rigorous treatment of complex mathematical objects such as wave functions and operators. Real analysis, which deals with the properties of real numbers and their functions, is also important in high energy physics as it provides the necessary tools for understanding the behavior of physical quantities.

In addition, many of the fundamental concepts and principles in theoretical high energy physics, such as symmetries and conservation laws, are deeply rooted in pure math. Without a strong foundation in pure math, it would be difficult to fully grasp and develop these concepts.

Therefore, it is highly recommended for anyone pursuing research in theoretical high energy physics to have a solid understanding of pure math, including functional analysis and real analysis. Even if your specific research does not require extensive use of these concepts, having a strong background in pure math will greatly enhance your ability to understand and contribute to the field.