Symmetry charge-conjugation

For a discussion of the transformation of the field operators under improper Lorentz transformations and discrete symmetry operations such as charge conjugation, see ... 

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. 

Once formed, the source dipole is a broken symmetry [2] in the vacuum s energy flux along the lines experimentally shown by Wu et al. in 1957 [35]. As Lee points out, the asymmetry between opposite signs of electric charge is called C violation, or charge conjugation violation, or sometimes particle-antiparticle asymmetry. As Nobelist Lee [2] further states, Since non-obser-vables imply symmetry, these discoveries of asymmetry must imply observables. ... 

Another type of symmetry of importance in elementary particle physics is that entitled charge conjugation. This principle slates that if each particle in a given isolated system is replaced by its corresponding anliparticle, then no difference can be observed. For example, if. in a hydrogen atom, the proton is replaced by an anti-proton and the electron is replaced hy a positron, then this antimatter atom will behave exactly like an ordinary atom, so long as it does not come inlo contact with ordinary atoms. 

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. 

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... 

Like any other great idea, the symmetry principle should be used with circumspection lest the need of enquiry beyond the search for symmetry is obscured. The hazard lurks therein that nowhere in the world has mathematically precise symmetry ever been encountered. The fundamental symmetries underpinning the laws of Nature, i.e. parity (P), charge conjugation (C), and time inversion (T), are hence no more than local approximations and, although the minor exceptions may be just about undetectable, they cannot be ignored2. 

The space-time symmetry underlying the Lewis model requires further analysis. It has often been speculated that the known universe is one of a pair of symmetry-related worlds. Naan argued forcefully [105] that an element of PCT (Parity-Charge conjugation-Time inversion) symmetry within the universal structure is indispensible to ensure existence. The implication is co-existence of material and anti-material worlds in an unspecified symmetric arrangement. Hence any interaction in the material world must be mirrored in the anti-world and it will be shown that this accords with the suggested mechanism of interaction. 

The demise of the parity principle brought down another symmetry principle that goes by the awkward name of charge conjugation. This principle, C symmetry, simply means that the same laws that describe a process involving matter will also describe the same process involving antimatter. In fact, however, the violation... 

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

It is easy to show that (141) preserves charge conjugation symmetry in the free particle problem. But perhaps what is just as important is that spinor basis sets satisfying (141) listed below generate no spurious solutions for JC > 0 of the sort reported by [39,41,42,91,92]. 

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. 

I note in passing that apart from the effects due to parity nonconservation, also effects that arise from nonconservation of the symmetry with respect to simultaneous spatial and temporal inversion, so-called VT-odd effects, or to simultaneous charge conjugation and spatial inversion, denoted CT -violating effects, received particular attention especially for diatomic molecules. Readers interested in VT- or CP-violating effects in molecular systems are referred to the book of Khriplovich [42] and to the reviews [32,43]. 

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]. 

Whereas energy appears to be distributed almost continuously, compared to matter, the distribution of matter presents the more tractable problem. When delving into the nature of matter, in its most elementary state, it is encountered in two antagonistic forms with equal probability. These two forms, called matter and anti-matter are best considered as the complementary forms of elementary stuff in two symmetry-related modes of existence. Symmetry-related units of matter and antimatter have the same mass but opposite electric charges and behave in opposite sense with respect to time. This relationship obeys the dictates of what is probably the most fundamental symmetry in Nature, known as CPT (charge conjugation-parity-time inversion) symmetry. Wherever it has been investigated, all natural phenomena have been found to obey CPT symmetry without exception. 

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. 

The most comprehensive symmetry that incorporates all of the foregoing is best known by the acronym CPT (charge conjugation - parity - time). Its most stringent demand is an exact balance between the matter and antimatter of the universe. 

Empirical evidence at variance with standard cosmology is, likewise, totally ignored. Even the most fundamental of empirical observations, known as universal CPT (charge conjugation-parity-time inversion) symmetry, which dictates equal amounts of matter and antimatter in the cosmos, is dismissed out-of-hand. Less well known, but of equal importance, cosmic self-similarity, is not considered at all. 

Here also, then, a very small initial asymmetry led seemingly to a complete dominance of the normal matter present today. The exact origin of the cosmic asymmetry is not known [14]. However, we know a small fundamental asymmetry in the so-called charge conjugation (C) and also in the combination CP of charge conjugation with parity (P). Hypotheses exist, which make this fundamental asymmetry responsible for the nearly complete asymmetry observed in the cosmos today, but their validity is doubtful. This question, thus, also remains open at the time. We shall address these symmetries in more detail below. 

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... 

This therefore corresponds to exchanging particles and antiparticles. Such a symmetry operation is called the charge conjugation and denoted as C symmetry. This symmetry will be not marked in the wave function symbol (because as a rule, we are dealing with matter, not antimatter), but we will want to remember it later. Sometimes it may turn out unexpectedly to be useful (see Chapter 13, p. 820). After Wu s experiment, physicists tried to save the hypothesis that what is conserved is the CP symmetry i.e., the product of charge conjugation and inversion. However, analysis of experiments with the meson K decay has shown that even this symmetry is approximate (although the deviation is extremely small). 

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