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 — advanced_tools:group_theory:lie_groups [2017/12/17 10:23] (current) 2017/12/17 11:23 jakobadmin created 2017/12/17 11:23 jakobadmin created Line 1: Line 1: + ====== Lie Groups ====== + +  ​ + + Lie groups describe continuous symmetry and lie at the heart of modern physics. For example, the symmetry group of the [[models:​standard_model|standard model of particle physics]] and the best spacetime symmetry group that we know (the Poincare group) are Lie groups. ​ + +  ​ + + A Lie group is a continuous set of transformations that satisfy the [[advanced_tools:​group_theory:​|group axioms]]. A good example for a Lie group is the symmetry group of the circle. A rotation by $5^\circ$ is a symmetry of the circle and a rotation by $0.00001^\circ$ is a symmetry, too. In contrast, the symmetry group of a square is not continuous. A rotation by $90^\circ$ is a symmetry, whereas a rotation by $5^\circ$ is not a symmetry. + ​ +  ​ + + See the recommendations [[advanced_tools:​group_theory|here]]. ​ + +  ​ + + + The motto in this section is: //the higher the level of abstraction,​ the better//. + ​ + + ​ +  ​ + + --> Example1# + + + <-- + + --> Example2:# + + + <-- + +  ​ + ​ +  ​ + + ​ + 