Charge conjugation is a concept in theoretical physics, particularly in the realm of particle physics and quantum field theory. It is an operation that involves changing the sign of the electric charge (and other related quantum numbers) of a particle or a quantum field.

Here are the key points about charge conjugation:

Electric Charge Reversal: Charge conjugation, often denoted as C, is an operation that reverses the sign of the electric charge of a particle. For example, if you apply charge conjugation to a particle with charge +1 (e.g., a positron), it becomes a particle with charge -1 (e.g., an electron).
Quantum Numbers: In addition to reversing the electric charge, charge conjugation can also affect other related quantum numbers, such as the "strangeness" in the context of the strong force. The exact transformation rules depend on the specific quantum field theory and the particles involved.
CPT Symmetry: Charge conjugation is often discussed in the context of a broader symmetry known as CPT symmetry. CPT stands for Charge, Parity, and Time reversal. CPT symmetry states that if you simultaneously reverse the electric charge (C), reverse spatial coordinates (P for Parity), and reverse the direction of time (T for Time), the laws of physics should remain unchanged. CPT symmetry is a fundamental principle in quantum field theory and is expected to hold in the Standard Model of particle physics.
Violation of CP Symmetry: While CPT symmetry is expected to be conserved, the CP symmetry (Charge conjugation combined with Parity reversal) is not always conserved. In certain particle interactions involving the weak force, such as some decays of neutral K mesons, CP violation has been observed. This discovery played a crucial role in understanding the violation of symmetries in particle physics and contributed to the development of the theory of the weak interaction.

In summary, charge conjugation is an operation that reverses the sign of the electric charge (and potentially other quantum numbers) of particles or fields. It is an important concept in the study of symmetries and interactions in particle physics and quantum field theory, particularly in the context of CPT symmetry and the exploration of CP violation.

The plane wave solution in the box normalisation is

The equation 1 satisfies the equation if

(E - m_oc²)uo = p²/ 2m_o (u_o + v_o)

And (E + m_oc²)v_o = - p²/ 2m_o (u_o + v_o)

For E = ± Ep, the function l 𝜓 ± > have two components. With the normalisation,

uo* ± uo ± - vo* ± vo ± = ± 1

Thus l 𝜓 + > (l 𝜓 - >) refers to the free motion of a particle in a +ve (-ve) isospin sate.

The equation 1 refers to a positive charge solution then

where l 𝜓 c > is called the charge conjugate solution with respect to l 𝜓 >. The transformation l 𝜓 > -> l 𝜓 c > implies

u_o + -> Vo- , Vo+ -> uo-, P-> - P, E-> - E

If l 𝜓 > refers to a particle, then l 𝜓 c > refers to its antiparticle. When an antiparticle is identical with the particle, we have a zero spin neutral particle.

Let l 𝜓_c > = E_1 l 𝜓 *> = 𝜆 l 𝜓 >

A two fold charge conjugate give back the original state requiring

𝜆² = 1 => 𝜆 = ± 1.

There are neutral particle with positive charge parity (𝜆 = + 1) or with the negative charge parity (𝜆 = - 1)

u = v*

It is called positive charge parity

u = - v*

It is called negative charge parity

Thus the neutral particle like πo is described by a real wave function.

This note is a part of the Physics Repository.

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