pivoxa15 said:How useful is it to study commutative algebra for the understanding and development of string theory?
What about geometric group theory? Which is more useful for string theory and why?
josh1 said:There’s nothing about either of these fields of mathematics that distinguishes themselves from the rest of the mathematics that is needed either to master the basics of string theory as it’s currently presented in introductory treatments or to understand research papers. If you understand General Relativity, QFT and particle physics at the first year graduate level, than you know enough mathematics (and physics) to get through the most sophisticated texts on string theory.
pivoxa15 said:texts written by physicists?
pivoxa15 said:What about texts written by mathematicians? I suppose the title would be more along the lines of the mathematics of string theory.
pivoxa15 said:texts written by physicists?
pivoxa15 said:What about texts written by mathematicians? I suppose the title would be more along the lines of the mathematics of string theory.
Commutative Algebra is a branch of mathematics that studies the properties of commutative rings and modules over them. It includes topics such as ideals, polynomial rings, prime and maximal ideals, and localization. In string theory, commutative algebra is used to describe the algebraic structures of spacetime.
Geometric Group Theory is a field that combines group theory and geometry to study discrete groups and their actions on geometric spaces. In string theory, geometric group theory is used to understand the symmetries and transformations of spacetime.
Commutative Algebra and Geometric Group Theory are both used in string theory to study the algebraic and geometric structures of spacetime. They provide the mathematical framework for understanding the symmetries and transformations of string theory, which are essential for making predictions and calculations.
Commutative Algebra and Geometric Group Theory are used in string theory to study topics such as D-branes, mirror symmetry, and moduli spaces. They are also used to understand the mathematical foundations of superstring theories and their connections to other areas of mathematics.
There are many resources available for learning about Commutative Algebra and Geometric Group Theory for String Theory, including textbooks, online lectures, and research articles. It is recommended to have a strong foundation in abstract algebra and group theory before diving into these topics. Additionally, attending conferences and workshops on string theory can provide opportunities to learn from experts in the field.