Symmetries and particle physics

Symmetries in physics provide a great fascination to us – one of the hang-ups of mankind. We can recognise a symmetry easily, and they provide a great tool to classify shapes and patterns. There is an important area of mathematics called group theory, where one studies the transformations under which an object is symmetric. In order to make this statement seem less abstract, let me look at a simple example, a regular hexagon in a plane. As can be seen in ﬁgure Fig. 8.5 , this object is symmetric (i.e., we can’t distinguish the new from the old object) under rotations around centre over angles of a multiple of $6{0}^{\circ}$, and under reﬂection in any of the six axes sketched in the second part of the ﬁgure.

8.1
Importance of symmetries:
Noether’s theorem

8.2 Lorenz and Poincaré invariance

8.3 Internal and space-time symmetries

8.4 Discrete Symmetries

8.4.1 Parity $P$

8.4.2 Charge conjugation $C$

8.4.3 Time reversal $T$

8.5 The $CPT$ Theorem

8.6 $CP$ violation

8.7 Continuous symmetries

8.7.1 Translations

8.7.2 Rotations

8.7.3 Further study of rotational symmetry

8.8 symmetries and selection rules

8.9 Representations of SU(3) and multiplication rules

8.10 broken symmetries

8.11 Gauge symmetries

8.2 Lorenz and Poincaré invariance

8.3 Internal and space-time symmetries

8.4 Discrete Symmetries

8.4.1 Parity $P$

8.4.2 Charge conjugation $C$

8.4.3 Time reversal $T$

8.5 The $CPT$ Theorem

8.6 $CP$ violation

8.7 Continuous symmetries

8.7.1 Translations

8.7.2 Rotations

8.7.3 Further study of rotational symmetry

8.8 symmetries and selection rules

8.9 Representations of SU(3) and multiplication rules

8.10 broken symmetries

8.11 Gauge symmetries