Charge conjugation invariance

Four-photon decay of orthopositronium a test of charge-conjugation invariance. Phys. Rev. A 54 1952-1956. 

Parapositronium (p-Ps) is the spin 0 state of Ps, which decays with rate As into an even number of photons due to charge conjugation invariance. The decay into four photons is significantly suppressed [21] and can be ignored at the current experimental level. The two photon decay rate, A2, is calculated using perturbation theory and has been recently calculated [4] through order (n)2 to be1 7989.50 0.02 ps-1. 

The transition 23S i — 24Pl is normally forbidden by charge-conjugation invariance, but with the application of a small static magnetic field the Zeeman-... 

Moreover, both the Lagrangian and the electronic four current have been written in a charge conjugation invariant form [27], i.e. under the charge conjugation (transforming electrons into positrons and vice versa) the four... 

Invariance with Respect to Inversion-Parity Invariance with Respect to Charge Conjugation Invariance with Respect to the Symmetry of the Nuclear Framework Conservation of Total Spin Indices of Spectroscopic States... 

Invariance of Quantum Electrodynamics under Discrete Transformations.—In the present section we consider the invariance of quantum electrodynamics under discrete symmetry operations, such as space-inversion, time-inversion, and charge conjugation. 

The above transformation properties of the current operator make quantum electrodynamics invariant under the operation Ue, usually called charge conjugation, provided... 

The invariance of quantum electrodynamics under charge conjugation has several immediate consequences. 

The invariance of the theory under charge conjugation implies that... 

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. 

Wolfenstein, L. and Ravenhall, D.G. (1952). Some consequences of invariance under charge conjugation. Phys. Rev. 88 279-282. 

Among the mostly fundamentally assumed symmetries in nature are the Lorentz invariance and the validity of the CPT theorem which demands an invariance of nature under simultaneous charge conjugation (C), parity operation... 

The operator C is called charge conjugation. As an antiunitary transformation it is a symmetry transformation, that is, all transition probabilities are left invariant. 

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. 

Lorentz transformations is also invariant under the combined operations of charge conjugation, C, space inversion, P, and time reversal, T, taken in any order. 

The Hiickel model as applied to polyenes possesses a symmetry known as alternancy symmetry, since the polyene system can be subdivided into two sublattices such that the Hiickel resonance integral involves sites on different sublattices. In such systems, the Hamiltonian remains invariant when the creation and annihilation operators at each site are interchanged with a phase of +1 for sites on one sublattice and a phase of -1 on sites of the other. Even in interacting models this symmetry exists when the system is half-filled. The alternancy symmetry is known variously as electron-hole symmetry or charge-conjugation symmetry [16]. 

The Estonian academician G.I. Naan (1964), on the basis of the Bohr-Liiders (1954) theorem, argued that the universe cannot exist without an element of CPT (Charge conjugation-Parity-Time) inversion symmetry, which implies the co-existence of material and anti-material worlds. Any interaction in the material world must be mirrored in the anti-world, but without direct contact between the two domains. Because of the inversion symmetry all conservation laws are automatically satisfied as invariant, at magnitudes of zero. 

CP invariance The symmetry generated by the combined operation of changing charge conjugation (Q and parity (P). CP violation occurs in weak interactions in kaon decay and in B-mesons. See also CPT theorem time reversal. 

If a Hamiltonian has particle-hole (or charge-conjugation) S3unmetry then it is invariant under the transformation of a particle into a hole under the action of the particle-hole operator, J ... 

The conclusion of these works is that the parity (P) invariance and, separately, the charge conjugation (C) invariance are violated in P decay, while the time reversal (T) or combined CP invariance is not. The parity non-invariance (i.e., non-invariance of the Hamiltonian of the weak interaction under space reflection) can be expressed alternativelyby saying that the parity is not conserved. This formulation is a consequence of the fact that the parity P is an observable quantity. The presence of two-pion decay mode in the K° kaon decay implies, however, that even the CP invariance is violated in the weak interaction (Christenson et al. 1964). 

These invariance relations, when treated literally and rigorously, are not of particular usefulness in theoretical chemistry. They may, however, open new possibilities when considered as some limiting cases. Chemical reaction mechanisms very often involve the interaction of molecular ions. Suppose we have a particular reaction mechanism. Now, let us make the charge conjugation of all the objects involved in the reaction (this would require the change of matter to antimatter). 

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