C-symmetry

Encyclopedia : C : CS : CSY : C-symmetry

In physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry maximally.

Charge Reversal in Electromagnetism

The laws of electromagnetism (both classical and quantum) are invariant under this transformation: if each charge q were to be replaced with a charge -q and the directions of the electric and magnetic fields were reversed, the dynamics would preserve the same form. In the language of quantum field theory, charge conjugation transforms:

[\psi \rightarrow -i(\bar\psi \gamma^0 \gamma^2)^T]
[\bar\psi \rightarrow -i(\gamma^0 \gamma^2 \psi)^T]
[A^\mu \rightarrow -A^\mu]

Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in the Standard Model. This property is what is meant by the "maximal violation" of C-symmetry in the weak interaction.

(Some postulated extensions of the Standard Model, like left-right models, restore this C-symmetry.)

Combination of Charge and Parity Reversal

It was believed for some time that C-symmetry could be combined with the parity-inversion transformation (see P-symmetry) to preserve a combined CP-symmetry. However, violations of even this symmetry have now been identified in the weak interactions (particularly in the kaons and B mesons). In the Standard Model, this CP violation is due to a single phase in the CKM matrix. If CP is combined with time reversal (T-symmetry), the resulting CPT-symmetry can be shown using only the Wightman axioms to be universally obeyed.

Ambiguity in Charge Definition

There is really a lot of ambiguity and arbitrariness in the definition of charge conjugation. To give an example, take two real scalar fields, φ and χ. Formulated as it is, both fields have even C-parity. Now reformulate things so that [\psi\equiv }]. Now, φ has an even C-parity whereas χ has an odd C-parity. But let's redefine [\psi\equiv }]. Now it's the other way around. Similarly, a complex Weyl spinor can be reexpressed as a real Majorana spinor and vice versa. This arbitrariness allows physicists to define C the way it is in left-right models.

C, P and T Symmetries [http://encycl.opentopia.com/ edit ]
C-symmetry | P-symmetry | T-symmetry
CP-symmetry | CPT symmetry
pin group

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.

C, P and T Symmetries	[http://encycl.opentopia.com/ edit ]
C-symmetry \| P-symmetry \| T-symmetry
CP-symmetry \| CPT symmetry
pin group