Feynman slash notation

In the study of <a href="/facts/Fermionic_field/KKaGVgX6">Dirac fields</a> in <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, <a href="/facts/Richard_Feynman/32vGFrtB">Richard Feynman</a> introduced the convenient Feynman slash notation (less commonly known as the <a href="/facts/Paul_Dirac/6bt5yRdk">Dirac</a> slash notation). If A is a <a href="/facts/Covariant_vector/s3HGMkhz">covariant vector</a> (i.e., a <a href="/facts/1-form/NQLbWmtD">1-form</a>),

A
          
          
          
          
            /
          
        
         
        
          
            
              
                =
              
              
                
                  d
                  e
                  f
                
              
            
          
        
         
        
          γ
          
            0
          
        
        
          A
          
            0
          
        
        +
        
          γ
          
            1
          
        
        
          A
          
            1
          
        
        +
        
          γ
          
            2
          
        
        
          A
          
            2
          
        
        +
        
          γ
          
            3
          
        
        
          A
          
            3
          
        
      
    
    {\displaystyle {A\!\!\!/}\ {\stackrel {\mathrm {def} }{=}}\ \gamma ^{0}A_{0}+\gamma ^{1}A_{1}+\gamma ^{2}A_{2}+\gamma ^{3}A_{3}}

where γ are the <a href="/facts/Gamma_matrices/C2y9Aumy">gamma matrices</a>. Using the <a href="/facts/Einstein_summation_notation/UXwS43wU">Einstein summation notation</a>, the expression is simply

A
          
          
          
          
            /
          
        
         
        
          
            
              
                =
              
              
                
                  d
                  e
                  f
                
              
            
          
        
         
        
          γ
          
            μ
          
        
        
          A
          
            μ
          
        
      
    
    {\displaystyle {A\!\!\!/}\ {\stackrel {\mathrm {def} }{=}}\ \gamma ^{\mu }A_{\mu }}
  
.

Feynman slash notation open-in-new

Feynman slash notation