Symmetries & Conservation Laws

Symmetries and conservation laws are one of the most fundamental concepts in particle physics.

Symmetries

First, let’s define what we mean by symmetries.

In general, symmetries refer to the invariance of a physical system under certain transformations, such as rotation or reflection.

For example, the laws of physics are symmetric under rotations in three-dimensional space, meaning that the behavior of a physical system does not change if we rotate the system about its axis.

Symmetries can also be defined in terms of discrete transformations, which are mathematical functions that map one set of values to another set of values in a discrete manner.

A discrete transformation that preserves the symmetries of a physical system is called a symmetry transformation.

Conservation Laws

Conservation laws are another important concept in particle physics. These laws describe the conservation of certain quantities, such as energy, momentum, and angular momentum, during physical processes.

For example, the law of conservation of energy states that the total energy of a closed system remains constant over time, unless it is transferred to or from the system by some external force.

Relation between Symmetries and Conservation Laws

Conservation laws are closely related to symmetries, as many conservation laws can be derived from the symmetries of a physical system.

For example, the conservation of momentum can be derived from the symmetry of the laws of physics under translations in space.

NOTE – Conservation laws are always associated with some kind of symmetry but the reverse is not always true.