Thanks!vanhees71 said:J. C. Taylor, Gauge Theories of Weak Interactions, Cambridge University Press, 1976.
D. Bailin and A. Love, Introduction to Gauge Field Theory, Adam Hilger, Bristol and Boston, 1986.
M. D. Schwartz, Quantum field theory and the Standard Model, Cambridge University Press, Cambridge, New York, 2014.
Classical and quantum Yang-Mills theories are mathematical frameworks used to describe the interactions between elementary particles. They are based on the concept of gauge symmetry, which refers to the idea that the laws of physics should remain the same regardless of certain mathematical transformations.
The non-abelian aspect of Yang-Mills theories refers to the fact that the theory involves interactions between particles that carry charges of different types, known as non-abelian charges. This is in contrast to abelian theories, which only involve interactions between particles with the same type of charge.
Some resources for studying classical and quantum Yang-Mills theories include textbooks, research papers, online lectures and courses, and conferences and workshops. Additionally, there are many online forums and communities where experts and enthusiasts discuss and share information about these theories.
Classical and quantum Yang-Mills theories are related because the classical theory serves as the foundation for the quantum version. Classical Yang-Mills theory describes the behavior of particles at a macroscopic level, while quantum Yang-Mills theory takes into account the microscopic behavior of particles and their interactions.
Some current research topics in classical and quantum Yang-Mills theories include the study of confinement and asymptotic freedom, the formulation of new mathematical methods for solving these theories, and the exploration of their connections to other areas of physics such as string theory and gravity. Other areas of interest include the application of these theories to cosmology and the study of topological phases of matter.