pariteetti

Pariteetti, or parity, is a concept describing symmetry under a sign change or spatial inversion. In mathematics it refers to the evenness or oddness of objects, while in physics it describes how a system or state transforms under the parity operation that inverts spatial coordinates.

In mathematics, pariteetti classifies integers as even or odd: an integer is even if it is divisible by 2, and odd otherwise. For functions, parity means f(-x) equals f(x) (even) or f(-x) equals -f(x) (odd). Pariteetti informs symmetry properties used in analysis, such as Fourier expansions, and in modular arithmetic and group theory.

In physics, parity is the eigenproperty of the parity operator, which flips spatial coordinates: Pψ(r) = ψ(-r). States with definite parity have eigenvalues +1 (even) or -1 (odd). If the Hamiltonian commutes with parity, parity is conserved; otherwise it can be violated. Pariteetti determines selection rules for transitions: electric-dipole (E1) transitions connect states of opposite parity, while magnetic-dipole (M1) or electric-quadrupole (E2) transitions may have different parity behavior. In molecular and crystallographic contexts, parity classification (gerade/ungerade in centrosymmetric systems) helps predict spectra and bonding characteristics. In quantum field theory, parity is a fundamental symmetry that can be exact or violated depending on the interactions considered.

A historic landmark is the discovery of parity violation in weak interactions, demonstrated in beta decay experiments in 1957, which showed that nature is not invariant under spatial inversion in all processes. The concept of pariteetti remains essential across physics and mathematics as a compact description of symmetry properties and their consequences for physical phenomena.