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.
Parity is a somewhat subtle mathematical concept concerned with the positions and motions of groups of elementary particles such as protons, neutrons, electrons, neutrinos, mesons and others, including the recently discovered "anti" particles.
Parity is a measure of the appearance of a group of these particles if their positions and motions only are seen reflected in a mirror, leaving their directions of spin unchanged.
The law of conservation of parity states that, if an isolated group of elementary particles, whatever the size of the group, is fragmented, then the parity of all the fragments together is the same as that of the original group.
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