A conserved current is a vector field satisfying the continuity equation . Its spatial integral is constant in time when no current crosses the boundary.
An integral of the time component of a conserved current is a conserved charge when the spatial boundary flux vanishes. Charges need not come from an immediately apparent elementary symmetry; a field theory can have an infinite higher-derivative current hierarchy. A Noether charge is obtained from the symmetry current supplied by the Noether theorem.
In a massless four-dimensional theory, current conservation gives a transverse tensor structure, . With current mass dimension three, the scalar coefficient has dimension zero.
Articles by others on the same topic
In physics, particularly in the context of field theory and particle physics, a "conserved current" refers to a current that is associated with a conserved quantity in a dynamical system. This concept is heavily rooted in the principles of symmetry, notably through Noether's theorem, which connects symmetries of the action of a physical system to conserved quantities.