Charge-particle time invariance

After the discovery of the combined charge and space symmetry violation, or CP violation, in the decay of neutral mesons [2], the search for the EDMs of elementary particles has become one of the fundamental problems in physics. A permanent EDM is induced by the super-weak interactions that violate both space inversion symmetry and time reversal invariance [11], Considerable experimental efforts have been invested in probing for atomic EDMs (da) induced by EDMs of the proton, neutron, and electron, and by the P,T-odd interactions between them. The best available limit for the electron EDM, de, was obtained from atomic T1 experiments [12], which established an upper limit of de < 1.6 x 10 27e-cm. The benchmark upper limit on a nuclear EDM is obtained from the atomic EDM experiment on Iyt,Hg [13] as d ig < 2.1 x 10 2 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 24e-cm, was also obtained by Dmitriev and Senkov [14]. The previous upper limit on the proton EDM was estimated from the molecular T1F experiments by Hinds and co-workers [15]. 

However, the symmetry of the situation can be restored if we interchange the words right and "left in the description of the experiment at the same time that we exchange each particle with its antiparticle. In the above experiment, this is equivalent to replacing the word clockwise with counterclockwise. When this is done, the positrons arc emitted in the downward direction, just as the electrons m the original experiment. The laws of nature are thus found to be invariant to the simultaneous application of charge conjugation and mirror inversion. 

Time reversal invariance describes the fact that in reactions between elementary particles, it does not make any difference if the direction of the time coordinate is reversed. Since all reactions are invariant to simultaneous application of mirror inversion, charge conjugation, and time reversal, the combination of all three is called CPT symmetry and is considered to be a very fundamental symmetry of nature. 

Abstract. CPT invariance is a fundamental property of quantum field theories in flat space-time. Principal consequences include the predictions that particles and their antiparticles have equal masses and lifetimes, and equal and opposite electric charges and magnetic moments. It also follows that the fine structure, hyperfine structure, and Lamb shifts of matter and antimatter bound systems should be identical. 

It has already been shown that for constant a this invariance (symmetry) implies conservation of the charge of a free particle. In general relativity, which is based on a curved manifold rather than flat space with a globally fixed coordinate system, each point has its own coordinate system and hence its own gauge factor. This means that the gauge factor a is no longer a constant, but a function of space-time, i.e. 

The weak interactions that cause atomic PNC violate not only the symmetry of parity, P, but also the symmetry of charge conjugation, C. However, the product of these, CP, is conserved. Because any quantum field theory conserves CPT, where T is time reversal this is equivalent to saying that T is conserved. However, even this symmetry is known to be violated. To date, this incompletely understood phenomenon has been seen in only two systems, the neutral kaon system, and, quite recently, the neutral B meson system. However, as noted already in the 1950 s by Ramsey and Purcell [62], an elementary particle possessing an intrinsic electric dipole moment also violates T invariance, so that detection of such a moment would be a third way of seeing T noninvariance. 

CPT theorem - Atheorem in particle physics which states that any local Lagrangian theory that is invariant under proper Lorentz transformations is also invariant under the combined operations of charge conjugation, C, space inversion, P, and time reversal, T, taken in any order. 

An extremely interesting property of free antiparticles is that they can be treated mathematically as if they were particles of the same mass and of oppositely signed charge of the same absolute value going backward in space and time. This is the consequence of one of the most important symmetries of Nature CPT invariance (Kostelecky 2002). It states that the following three operations ... 

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