Conserved current
In physics a conserved current is a current, 
  
    
      
        
          j
          
            μ
          
        
      
    
    {\displaystyle j^{\mu }}
  
, that satisfies the continuity equation 
  
    
      
        
          ∂
          
            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 conserved quantity. In gauge theories the gauge fields couple to conserved currents. For example, the electromagnetic field couples to the conserved electric current.