In physics, parity transformation is the simultaneous sign flip of all coordinates:
The determinant of this transformation equals minus one. In even-dimensional spaces, it is usual to redefine the parity transformation so that it flips the sign of an odd number of coordinates, so that the determinant still equals minus one.
In quantum mechanics, the parity transformation P becomes an operator that squares to one:
As for every operator, it can be viewed as a physical quantity, also called the parity. Its eigenvalues are + 1 and - 1. In theories that exhibit a symmetry between the left and the right hand (such as Quantum electrodynamics), parity is conserved.