Symmetry in physics

A symmetry is a transformation that leaves a physical system or its laws unchanged. Symmetries constrain possible processes and, in many theories, correspond to conserved quantities.

Noether's theorem: A theorem linking continuous symmetries of a system's action to conserved quantities. It turns continuous invariances of physical laws into conservation laws.
Transformation (physics): A mapping that changes a physical description, state, or set of coordinates. Symmetry is defined by the transformations that preserve a system or its laws.
Rotational symmetry: Invariance under rotations about a point, axis, or set of axes. Rotational invariance of isolated systems is associated with angular momentum conservation.
Symmetry breaking: A reduction or loss of symmetry in a system or its governing description. It contrasts exact invariance with systems or states that exhibit fewer symmetries.
Conservation law: A rule stating that a measurable quantity remains constant during a system's evolution. Conserved quantities often arise from symmetries of the laws governing a system.
Invariant (physics): A quantity or property unchanged under a specified transformation. Invariance is the defining condition a symmetry transformation must satisfy.
Translational symmetry: Invariance under shifts of position or time by a fixed amount. Spatial and temporal translations connect to conservation of momentum and energy.
Gauge fixing: A choice of one representative from a set of gauge-equivalent mathematical descriptions. It handles descriptive redundancy rather than adding a physical symmetry.
Group theory: The mathematical study of sets of transformations closed under composition and inverses. Groups organize symmetry transformations and their relations.
State space: The set of all possible states of a physical system, represented by their independent variables. A symmetry may map one allowed state to another within the same space.

Linked from 8 pages