23.01.2014 Views

SYMMETRIES in PHYSICS

SYMMETRIES in PHYSICS

SYMMETRIES in PHYSICS

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Symmetry and Spontaneous Symmetry Break<strong>in</strong>g<br />

Selected Groups and Symmetries<br />

Spontaneous Symmetry Break<strong>in</strong>g<br />

Subgroup Structure Can Be Very, Very Rich ...<br />

32 Po<strong>in</strong>t Groups: Subgroups<br />

.<br />

D 4h<br />

T h<br />

O T d<br />

D 6h<br />

C 4h<br />

D 4<br />

D 2d<br />

C 4v<br />

D 2h<br />

T D 6<br />

C 6h<br />

C 6v<br />

D 3d<br />

D<br />

3h<br />

S 4<br />

C 4<br />

D 2<br />

C 2h<br />

C 2v<br />

C 6<br />

C 3i<br />

D 3<br />

C 3v<br />

C 3h<br />

O h<br />

C C C C<br />

i 2 s 3<br />

Figure: Richness of the sub-group<br />

structures at the end of cha<strong>in</strong>...<br />

C<br />

1<br />

.<br />

Dashed l<strong>in</strong>es <strong>in</strong>dicate that the<br />

subgroup marked is not <strong>in</strong>variant<br />

Trivial groups are denoted here<br />

C 1 ≡ {1I}, C s ≡ {1I, ˆσ},<br />

C i ≡ {1I, ˆπ}<br />

Here we show the structure only<br />

at the very end of the SU n cha<strong>in</strong><br />

- it helps imag<strong>in</strong><strong>in</strong>g how rich the<br />

full group structure is ...<br />

Jerzy DUDEK<br />

<strong>SYMMETRIES</strong> <strong>in</strong> <strong>PHYSICS</strong>

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!