## Parity (physics) |

In **parity transformation** (also called **parity inversion**) is the flip in the sign of *one*

It can also be thought of as a test for

A matrix representation of **P** (in any number of dimensions) has *not* a parity transformation; it is the same as a 180°-

In

- simple symmetry relations
- classical mechanics
- effect of spatial inversion on some variables of classical physics
- quantum mechanics
- many-particle systems: atoms, molecules, nuclei
- quantum field theory
- parity in the standard model
- see also
- references

Under

*projective* refers to the fact that if one projects out the phase of each state, where we recall that the overall phase of a quantum state is not an observable, then a projective representation reduces to an ordinary representation. All representations are also projective representations, but the converse is not true, therefore the projective representation condition on quantum states is weaker than the representation condition on classical states.

The projective representations of any group are isomorphic to the ordinary representations of a

If one adds to this a classification by parity, these can be extended, for example, into notions of

*scalars*(*P*= +1) and(pseudoscalars *P*= −1) which are rotationally invariant.*vectors*(*P*= −1) and*axial vectors*(also called) (pseudovectors *P*= +1) which both transform as vectors under rotation.

One can define **reflections** such as

which also have negative determinant and form a valid parity transformation. Then, combining them with rotations (or successively performing *x*-, *y*-, and *z*-reflections) one can recover the particular parity transformation defined earlier. The first parity transformation given does not work in an even number of dimensions, though, because it results in a positive determinant. In even dimensions only the latter example of a parity transformation (or any reflection of an odd number of coordinates) can be used.

Parity forms the