Light front quantization

<p>The light-front quantization
of <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theories</a>
provides a useful alternative to ordinary equal-time 
<a href="/facts/Quantization_(physics)/fvs2Jwpn">quantization</a>.  In
particular, it can lead to a <a href="/facts/Special_relativity/vsFFc63E">relativistic</a> description of <a href="/facts/Bound_state/NndW5JQl">bound systems</a>
in terms of <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum-mechanical</a> <a href="/facts/Wave_function/KgM5ykjY">wave functions</a>.  The quantization is
based on the choice of light-front coordinates,
where 
  
    
      
        
          x
          
            +
          
        
        ≡
        c
        t
        +
        z
      
    
    {\displaystyle x^{+}\equiv ct+z}
  
 plays the role of time and the corresponding spatial coordinate is 
  
    
      
        
          x
          
            −
          
        
        ≡
        c
        t
        −
        z
      
    
    {\displaystyle x^{-}\equiv ct-z}
  
.  Here, 
  
    
      
        t
      
    
    {\displaystyle t}
  
 is the ordinary time, 
  
    
      
        z
      
    
    {\displaystyle z}

is one <a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian coordinate</a>, and 
  
    
      
        c
      
    
    {\displaystyle c}
  
 is the speed of light.  The other two Cartesian coordinates, 
  
    
      
        x
      
    
    {\displaystyle x}
  
 and 
  
    
      
        y
      
    
    {\displaystyle y}
  
, are untouched and often called transverse or perpendicular, denoted by symbols of the type

x
                →
              
            
          
          
            ⊥
          
        
        =
        (
        x
        ,
        y
        )
      
    
    {\displaystyle {\vec {x}}_{\perp }=(x,y)}
  
.  The choice of the <a href="/facts/Frame_of_reference/15yYfB9M">frame of reference</a> where the time

t
      
    
    {\displaystyle t}
  
 and 
  
    
      
        z
      
    
    {\displaystyle z}
  
-axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others.
</p>

Light front quantization open-in-new

Light front quantization