Parity (physics)

In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection):

In a two-dimensional plane, a simultaneous flip of all coordinates in sign is not a parity transformation; it is the same as a 180° rotation.

Under rotations, classical geometrical objects can be classified into scalars, vectors, and tensors of higher rank.

Then, combining them with rotations (or successively performing x-, y-, and z-reflections) one can recover the particular parity transformation defined earlier.

An alternative way to write the above classification of scalars, pseudoscalars, vectors and pseudovectors is in terms of the representation space that each object transforms in.

In a 2 dimensional space, for example, when constrained to remain on the surface of a planet, some of the variables switch sides.

Classical variables whose signs flip when inverted in space inversion are predominantly vectors.

, which reverses the parity of a state twice, leaves the spacetime invariant, and so is an internal symmetry which rotates its eigenstates by phases

However this is not true for the beta decay of nuclei, because the weak nuclear interaction violates parity.

For example, the ground state of the nitrogen atom has the electron configuration 1s22s22p3, and is identified by the term symbol 4So, where the superscript o denotes odd parity.

The parity operation involves the inversion of electronic and nuclear spatial coordinates at the molecular center of mass.

Centrosymmetric molecules at equilibrium have a centre of symmetry at their midpoint (the nuclear center of mass).

The operation i involves the inversion of the electronic and vibrational displacement coordinates at the nuclear centre of mass.

For centrosymmetric molecules the operation i commutes with the rovibronic (rotation-vibration-electronic) Hamiltonian and can be used to label such states.

Electronic and vibrational states of centrosymmetric molecules are either unchanged by the operation i, or they are changed in sign by i.

The nuclear hyperfine Hamiltonian can mix the rotational levels of g and u vibronic states (called ortho-para mixing) and give rise to ortho-para transitions[8][9] In atomic nuclei, the state of each nucleon (proton or neutron) has even or odd parity, and nucleon configurations can be predicted using the nuclear shell model.

For simplicity we will assume that canonical quantization is used; the vacuum state is then invariant under parity by construction.

The invariance of the canonical quantization procedure can be worked out, and turns out to depend on the transformation of the annihilation operator:[citation needed]

(Details of spinors are dealt with in the article on the Dirac equation, where it is shown that fermions and antifermions have opposite intrinsic parity.)

Applying the parity operator twice leaves the coordinates unchanged, meaning that P2 must act as one of the internal symmetries of the theory, at most changing the phase of a state.

To see if the parity operator can always be defined to satisfy P2 = 1, consider the general case when P2 = Q for some internal symmetry Q present in the theory.

In 1954, a paper by William Chinowsky and Jack Steinberger demonstrated that the pion has negative parity.

[13] They studied the decay of an "atom" made from a deuteron (21H+) and a negatively charged pion (π− ) in a state with zero orbital angular momentum

An obscure 1928 experiment, undertaken by R. T. Cox, G. C. McIlwraith, and B. Kurrelmeyer, had in effect reported parity violation in weak decays, but, since the appropriate concepts had not yet been developed, those results had no impact.

[16] In 1929, Hermann Weyl explored, without any evidence, the existence of a two-component massless particle of spin one-half.

Wu, Ambler, Hayward, Hoppes, and Hudson (1957) found a clear violation of parity conservation in the beta decay of cobalt-60.

[20] Three of them, R. L. Garwin, L. M. Lederman, and R. M. Weinrich, modified an existing cyclotron experiment, and immediately verified the parity violation.

[21] They delayed publication of their results until after Wu's group was ready, and the two papers appeared back-to-back in the same physics journal.

In 2010, it was reported that physicists working with the Relativistic Heavy Ion Collider had created a short-lived parity symmetry-breaking bubble in quark–gluon plasmas.

An experiment conducted by several physicists in the STAR collaboration, suggested that parity may also be violated in the strong interaction.