SYMMETRIES in PHYSICS

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Symmetry and Spontaneous Symmetry Breaking Selected Groups and Symmetries Spontaneous Symmetry Breaking Symmetry Groups and Degeneracies of Levels Hamiltonian and a Group of Transformations Given Hamiltonian H and a point-group G = {O 1 , O 2 , . . . O f } Assume that G is a symmetry group of H i.e. [H, O k ] = 0 with k = 1, 2, . . . f Spectra and Group’s Irreducible Representations Let irreducible representations of G be {R 1 , R 2 , . . . R r } Let their dimensions be {d 1 , d 2 , . . . d r }, respectively Then the eigenvalues {ε ν } of the problem Hψ ν = ε ν ψ ν appear in multiplets d 1 -fold, d 2 -fold ... degenerate Jerzy DUDEK SYMMETRIES in PHYSICS
Symmetry and Spontaneous Symmetry Breaking Selected Groups and Symmetries Spontaneous Symmetry Breaking Point Groups - ... and What We Need to Remember Consider a group of symmetry of an equilateral triangle (group C 3v ) Two Types of Transformations - Observe Existence of a Fixed Point a 120 o b c C^ 3 240 o (C ^ 2 3) b a c Figure: This group contains rotations Ĉ3 and Ĉ 2 3 (120o and 240 o ), left, and three vertical reflections ˆσ va , ˆσ vb and ˆσ vc , right, in addition to 1I. Six Element Point Group: C 3v = {1I, Ĉ 3 , Ĉ 2 3 , ˆσ va , ˆσ vb , ˆσ vc } Jerzy DUDEK SYMMETRIES in PHYSICS
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SYMMETRIES in PHYSICS Jerzy DUDEK I
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Symmetry and Groups: Historical Asp
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SYMMETRIES in PHYSICS

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