SYMMETRIES in PHYSICS

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Symmetry and Spontaneous Symmetry Breaking Selected Groups and Symmetries Spontaneous Symmetry Breaking Arrival of the Theory of Continuous (Lie) Groups Sophus LIE (1842-1899) S. LIE A. Introduces new type of groups whose elements are continuous functions of some parameter(s) B. Most important for physics applications are groups of matrices C. Examples: GL n , SL n , U n , SU n , O n , Sp 2n ... Distinguished role in physics play the space-time Lie groups: Rotation, Lorentz and Poincaré, dimensions 3, 6 and 10, respectively, as well as the unitary and special unitary groups together with all their sub-groups Jerzy DUDEK SYMMETRIES in PHYSICS
Symmetry and Spontaneous Symmetry Breaking Selected Groups and Symmetries Spontaneous Symmetry Breaking About Special Unitary Groups: SU n Groups SU n ↔ n × n unitary matrices U ↔ [det(U) = 1] It turns out that these matrices can be expressed as U = exp [ ∑ ] p αβ ĝ αβ , pαβ ↔ real parameters αβ Constant operators (generators) ĝ αβ satisfy [ ĝ αβ , ĝ γδ ] = δ βγ ĝ αδ − δ αδ ĝ γβ Jerzy DUDEK SYMMETRIES in PHYSICS
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SYMMETRIES in PHYSICS

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