In
physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
,
Csymmetry means the symmetry of physical laws under a
chargeIn physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.Formal definition:...
conjugation
transformationIn mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself that preserves this structure.Examples include...
. Electromagnetism, gravity and the strong interaction all obey Csymmetry, but
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
s violate Csymmetry.
Charge reversal in electromagnetism
The laws of
electromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
(both
classicalWhat "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
and
quantumIn physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
) are
invariantIn mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.Examples:In the current era, the immobility of polaris under the diurnal motion of the celestial sphere is a classical illustration of physical invariance.Another...
under this transformation: if each charge
q were to be replaced with a charge −
q and the directions of the
electricIn physics, an electric field surrounds electrically charged particles and timevarying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and
magnetic fieldA magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s were reversed, the dynamics would preserve the same form. In the language of
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
, charge conjugation transforms:



Notice that these transformations do not alter the
chiralityA chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
of particles. A lefthanded
neutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a halfinteger spin, chirality and a disputed but small nonzero mass. It is able to pass through ordinary matter almost unaffected...
would be taken by charge conjugation into a lefthanded antineutrino, which does not interact in the Standard Model. This property is what is meant by the "maximal violation" of Csymmetry in the weak interaction.
(Some postulated extensions of the
Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, like leftright models, restore this Csymmetry.)
Combination of charge and parity reversal
It was believed for some time that Csymmetry could be combined with the
parityIn physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
inversion transformation (see Psymmetry) to preserve a combined CPsymmetry. However, violations of even this symmetry have now been identified in the weak interactions (particularly in the
kaonIn particle physics, a kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness...
s and B
mesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of subparticles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s). In the Standard Model, this
CP violationIn particle physics, CP violation is a violation of the postulated CPsymmetry: the combination of Csymmetry and Psymmetry . CPsymmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
is due to a single phase in the CKM matrix. If CP is combined with time reversal (
TsymmetryT Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...
), the resulting CPTsymmetry can be shown using only the
Wightman axiomsIn physics the Wightman axioms are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s but they were first published only in 1964, after HaagRuelle scattering theory affirmed their significance.The axioms exist in...
to be universally obeyed.
Charge definition
To give an example, take two real scalar fields,
φ and
χ. Suppose both fields have even Cparity (even Cparity refers to even symmetry under charge conjugation ex.
, as opposed to odd Cparity which refers to antisymmetry under charge conjugation ex.
). Now reformulate things so that
. Now,
φ and
χ have even Cparities because the imaginary number
i has an odd Cparity (C is antiunitary).
In other models, it is possible for both
φ and
χ to have odd Cparities.