Light-front quantization applications

<p>The <a href="/facts/Light_front_quantization/rJ5Ry83I">light-front quantization</a> 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 a <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. The basic formalism is discussed <a href="/facts/Light_front_quantization/rJ5Ry83I">elsewhere</a>.
</p><p>There are many applications of this technique, some of which are discussed below. Essentially, the analysis of any relativistic quantum system can benefit from the use of light-front coordinates and the associated quantization of the theory that governs the system.
</p>

Light-front quantization applications open-in-new

Light-front quantization applications