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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, a charge may refer to one of many different quantities, such as the electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 in electromagnetism
Electromagnetism

Electromagnetism is the physics of the electromagnetic field, a field which exerts a force on Elementary particles with the property of electric charge and which is reciprocally affected by the presence and motion of such particles....
 or the color charge
Color charge

In particle physics, color charge is a property of quarks and gluons which are related to their strong interactions in the context of quantum chromodynamics ....
 in quantum chromodynamics
Quantum chromodynamics

Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
. Charges are associated with conserved quantum number
Quantum number

Quantum numbers describe values of conserved numbers in the dynamics of the quantum system. They often describe specifically the energies of electrons in atoms, but other possibilities include angular momentum, Spin etc....
s.

abstractly, a charge is any generator
Generating set of a group

In abstract algebra, a generating set of a group is a subset S such that every element of G can be expressed as the product of finitely many elements of S and their inverses....
 of a continuous symmetry
Continuous symmetry

In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as Motion s, as opposed to e.g....
 of the physical system under study. When a physical system has a symmetry of some sort, Noether's theorem
Noether's theorem

Noether's theorem states that any derivative Symmetry in physics of the action of a physical system has a corresponding conservation law. The action of a physical system is an integral of a so-called Lagrangian function, from which the system's behavior can be determined by the principle of least action....
 implies the existence of a conserved current
Conserved current

In physics a conserved current is a current, , that satisfies the continuity equation . The continuity equation represents a conservation law, hence the name....
. The thing that "flows" in the current is the "charge", the charge is the generator of the (local) symmetry group.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, a charge may refer to one of many different quantities, such as the electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 in electromagnetism
Electromagnetism

Electromagnetism is the physics of the electromagnetic field, a field which exerts a force on Elementary particles with the property of electric charge and which is reciprocally affected by the presence and motion of such particles....
 or the color charge
Color charge

In particle physics, color charge is a property of quarks and gluons which are related to their strong interactions in the context of quantum chromodynamics ....
 in quantum chromodynamics
Quantum chromodynamics

Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
. Charges are associated with conserved quantum number
Quantum number

Quantum numbers describe values of conserved numbers in the dynamics of the quantum system. They often describe specifically the energies of electrons in atoms, but other possibilities include angular momentum, Spin etc....
s.

Formal definition

More abstractly, a charge is any generator
Generating set of a group

In abstract algebra, a generating set of a group is a subset S such that every element of G can be expressed as the product of finitely many elements of S and their inverses....
 of a continuous symmetry
Continuous symmetry

In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as Motion s, as opposed to e.g....
 of the physical system under study. When a physical system has a symmetry of some sort, Noether's theorem
Noether's theorem

Noether's theorem states that any derivative Symmetry in physics of the action of a physical system has a corresponding conservation law. The action of a physical system is an integral of a so-called Lagrangian function, from which the system's behavior can be determined by the principle of least action....
 implies the existence of a conserved current
Conserved current

In physics a conserved current is a current, , that satisfies the continuity equation . The continuity equation represents a conservation law, hence the name....
. The thing that "flows" in the current is the "charge", the charge is the generator of the (local) symmetry group. This charge is sometimes called the Noether charge.

Thus, for example, the electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 is the generator of the U(1) symmetry of electromagnetism
Electromagnetism

Electromagnetism is the physics of the electromagnetic field, a field which exerts a force on Elementary particles with the property of electric charge and which is reciprocally affected by the presence and motion of such particles....
. The conserved current is the electric current
Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
.

In the case of local, dynamical symmetries, associated with every charge is a gauge field; when quantized, the gauge field becomes a gauge boson
Gauge boson

In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental interactions of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles....
. The charges of the theory "radiate" the gauge field. Thus, for example, the gauge field of electromagnetism is the electromagnetic field
Electromagnetic field

The electromagnetic field is a physical field produced by electric charge. It affects the behavior of charged objects in the vicinity of the field....
; and the gauge boson is the photon
Photon

In physics, the photon is an elementary particle, the quantum of the electromagnetic field and the basic unit of light and all other forms of electromagnetic radiation....
.

Sometimes, the word "charge" is used as a synonym for "generator" in referring to the generator of the symmetry. More precisely, when the symmetry group is a Lie group
Lie group

In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the Differential structure....
, then the charges are understood to correspond to the root system
Root system

In mathematics, a root system is a configuration of vector spaces in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras....
 of the Lie group; the discreteness of the root system accounting for the quantization of the charge.