Trigonometric tables

2013-05-21T20:41:10Z

117.239.242.130: /* Half-angle and angle-addition formulas */

{{Refimprove|date=December 2008}}

In [[physics]], '''C-symmetry''' means the symmetry of physical laws under a [[charge (physics)|charge]]-conjugation [[transformation (mathematics)|transformation]]. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but [[weak interaction]]s violate C-symmetry.

==Charge reversal in electromagnetism==
The laws of [[electromagnetism]] (both [[classical physics|classical]] and [[quantum]]) are [[Invariant (physics)|invariant]] under this transformation: if each charge ''q'' were to be replaced with a charge −''q'', and thus the directions of the [[electric field|electric]] and [[magnetic field]]s were reversed, the dynamics would preserve the same form. In the language of [[quantum field theory]], charge conjugation transforms:<ref name="PS">{{cite book|author=Peskin, M.E. and Schroeder, D.V.|title=An Introduction to Quantum Field Theory|publisher=Addison Wesley|year=1997|isbn=0-201-50397-2}}</ref>

# <math>\psi \rightarrow -i(\bar\psi \gamma^0 \gamma^2)^T</math>
# <math>\bar\psi \rightarrow -i(\gamma^0 \gamma^2 \psi)^T</math>
# <math>A^\mu \rightarrow -A^\mu</math>

Notice that these transformations do not alter the [[Chirality (physics)|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 model]]s, 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 (physics)|parity]]-inversion transformation (see [[P-symmetry]]) to preserve a combined [[CP-symmetry]]. However, violations of this symmetry have been identified in the weak interactions (particularly in the [[kaon]]s and B [[meson]]s). 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.

==Charge definition==
To give an example, take two real scalar fields, ''φ'' and ''χ''. Suppose both fields have even C-parity (even C-parity refers to even symmetry under charge conjugation ex. <math>C\psi(q) = C\psi(-q)</math>, as opposed to odd C-parity which refers to antisymmetry under charge conjugation ex. <math>C\psi(q)=-C\psi(-q)</math>). Now reformulate things so that <math>\psi\ \stackrel{\mathrm{def}}{=}\ {\phi + i \chi\over \sqrt{2}}</math>. Now, ''φ'' and ''χ'' have even C-parities because the imaginary number ''i'' has an odd C-parity (C is antiunitary).{{Clarify|date=January 2011}}

In other models, it is possible for both ''φ'' and ''χ'' to have odd C-parities.{{Clarify|date=December 2008}}

==See also==
* [[C parity]]
* [[anti-particle]]
* [[antimatter]]

==References==
{{reflist}}
* {{cite book|author=Sozzi, M.S.|title=Discrete symmetries and CP violation|publisher=Oxford University Press|year=2008|isbn=978-0-19-929666-8}}


{{C, P and T}}


[[Category:Quantum field theory]]
[[Category:Symmetry]]

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