I would say that, first of all, you need to learn about Hilbert spaces and group theoryPispi Choudhury said:Summary:: What are the relevant mathematics/ mathematical physics courses for studying quantum field theory and statistical field theory?
I'm a physics undergraduate currently in my junior(third) year, thanks.
Thank you so much !jedishrfu said:Quora has a list for you:
https://www.quora.com/What-are-the-...s-for-quantum-field-theory-in-ascending-order
and Stack has a similar list:
https://physics.stackexchange.com/questions/147024/what-kind-of-math-is-used-in-qft
Thank you !Gaussian97 said:I would say that, first of all, you need to learn about Hilbert spaces and group theory
Quantum field theory deals with the study of particles and their interactions at a microscopic level, while statistical field theory focuses on the behavior of large systems of particles at a macroscopic level. In quantum field theory, particles are described as excitations of quantum fields, while in statistical field theory, particles are treated as statistical ensembles.
A strong background in mathematics, particularly in calculus, linear algebra, and differential equations, is essential for understanding the concepts in quantum and statistical field theory. Knowledge of classical mechanics and electromagnetism is also important.
Quantum field theory is used in many areas of physics, such as particle physics, condensed matter physics, and cosmology. It has also found applications in technology, including the development of quantum computers. Statistical field theory is used in fields such as statistical mechanics, thermodynamics, and materials science.
Yes, there are still many open problems in both quantum and statistical field theory. Some of the current research topics include the unification of quantum field theory and general relativity, the nature of dark matter and dark energy, and the behavior of quantum systems at extreme temperatures and energies.
In addition to taking relevant courses in mathematics and physics, it is important to gain research experience through internships or undergraduate research projects. It is also helpful to stay updated on current developments in the field through attending conferences and reading scientific journals. Pursuing a graduate degree in physics or a related field is also beneficial for a career in quantum and statistical field theory.