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advanced_tools:group_theory:lie_groups

Lie groups describe continuous symmetry and lie at the heart of modern physics. For example, the symmetry group of the 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 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 here.

The motto in this section is: *the higher the level of abstraction, the better*.

- Example1

- Example2:

advanced_tools/group_theory/lie_groups.txt · Last modified: 2017/12/17 10:23 (external edit)

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