hokhani said:please prefer me a book or booklet or ...that at least includes one section or more about the subject of group theory in physics as i can understand the elements considered in this book about group theory:
"Mathematics method for physisists by George Arfken"
I'd like it was elementary and informative and also short.
Group theory is a branch of mathematics that studies the symmetry and structure of objects and systems. In physics, it is used to describe the laws of nature and the behavior of physical systems by studying the transformations that leave these laws unchanged.
Group theory is essential in physics because it provides a powerful framework for understanding the underlying symmetries and patterns in physical systems. It allows for the classification and prediction of physical phenomena, as well as the development of new theories and models.
Group theory is used in various areas of physics, such as quantum mechanics, particle physics, and solid state physics. Some examples include the rotation and translation symmetries of molecules, the symmetries of atomic orbitals, and the symmetries of fundamental particles.
In physics, group theory is applied through the use of mathematical tools such as group representations, character tables, and group generators. These tools are used to analyze the symmetries of physical systems and to make predictions about their behavior.
One of the challenges of using group theory in physics is the complexity of the mathematical concepts involved. It can also be challenging to find the appropriate group to describe a particular physical system, as well as to apply group theory to systems with continuous symmetries. Additionally, the limitations of current mathematical techniques may make it difficult to fully understand the symmetries of some physical systems.