Conserved current

In <a href="/facts/Physics/a7aH2y08">physics</a> a conserved current is a current, 
 
 
 
 
 j
 
 μ
 
 
 
 
 {\displaystyle j^{\mu }}
 
, that satisfies the <a href="/facts/Continuity_equation/GVav2Vet">continuity equation</a> 
 
 
 
 
 ∂
 
 μ
 
 
 
 j
 
 μ
 
 
 =
 0
 
 
 {\displaystyle \partial _{\mu }j^{\mu }=0}
 
. The continuity equation represents a conservation law, hence the name.
Indeed, integrating the continuity equation over a volume 
 
 
 
 V
 
 
 {\displaystyle V}
 
, large enough to have no net currents through its surface, leads to the conservation law
 
 
 
 
 
 ∂
 
 ∂
 t
 
 
 
 Q
 =
 0
 
 ,
 
 
 {\displaystyle {\frac {\partial }{\partial t}}Q=0\;,}
 
where 
 
 
 
 Q
 =
 
 ∫
 
 V
 
 
 
 j
 
 0
 
 
 d
 V
 
 
 {\textstyle Q=\int _{V}j^{0}dV}
 
 is the <a href="/facts/Charge_(physics)/jnQEDBI3">conserved quantity</a>.
In <a href="/facts/Gauge_theory/fSW3gggv">gauge theories</a> the gauge fields couple to conserved currents. For example, the <a href="/facts/Electromagnetic_field/MacraS8y">electromagnetic field</a> couples to the <a href="/facts/Charge_conservation/WGQXmoE8">conserved electric current</a>.

Conserved current open-in-new

Conserved current