Combined Inversion

Combined Inversion


the correlation of a physical system consisting of certain particles with another system consisting of the corresponding antiparticles and forming the mirror image of the former. Mathematically a combined inversion is the product of two operations: a charge conjugation C (the conversion from particles to antiparticles) and a space inversion P (the substitution of the particles’ coordinates — r for r).

In 1956, in connection with the discovery of the nonconservation of spatial parity in weak interactions, L. D. Landau and, independently, Li Tsung-tao and Yang Chen-ning formulated the hypothesis that any interactions in nature are invariant with respect to a combined inversion. Electromagnetic and strong interactions are identical for any original system and the system obtained by converting Cand P separately; therefore, they do not change during a combined inversion (CP). The weak interactions change during C and P operations but are identical for the systems obtained by one of the other CP conversions. For example, the disintegration of particles in response to a weak interaction looks like the mirror image of the disintegration of the corresponding antiparticles.

If a particle or a system of particles is absolutely neutral (that is, has zero values for the electric and baryon charges, for lepton charge, and for strangeness), then in the case of a combined inversion the corresponding particle or system of particles is the same. For example, the π0-meson, the K10 — and K20-mesons, the positronium (e+e), and the (π+π) system “are” absolutely neutral. For such particles and systems the concept of combined parity (parity with respect to a combined inversion) may be introduced, because when there are no forces in the system that change during a combined inversion, the wave function of the converted system either coincides with that of the original system or differs from it in sign. In the former case the system is said to have an even combined parity [like, for example, the K10-meson and the (π+π) system, which have an even orbital moment], and in the latter it is said to have an odd combined parity (such as the π0-meson and the K20-meson). The law for the conservation of combined parity prohibits, in particular, the disintegration of a K20-meson into two π0-mesons. The discovery in 1964 of the disintegration of the “long-lived” neutral kaons into two π-mesons revealed the existence of forces that changed during a combined inversion. The nature of these forces has not yet been definitely established.


Lee, T., and C. S. Wu. Slabye vzaimodeistviia. Moscow, 1968. (Translated from English.)


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The FAI group demonstrated greater error of the joint position than the control group only when the ankle was positioned at combined inversion and plantarflexion.
The FAI group underestimated plantarflexion angle when the ankle was placed at combined inversion and plantarflexion.

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