Factorization of the algebra of particles of half-odd spin

1952 ◽  
Vol 48 (1) ◽  
pp. 110-117
Author(s):  
K. J. Le Couteur
Keyword(s):  
Wave Equation ◽  
Direct Product ◽  
Matrix Algebra ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Original Matrix ◽  
Dirac Algebra ◽  
The Matrix ◽  
Integral Spin

AbstractIt is proved that the matrix algebra for any relativistic wave equation of half-odd integral spin can be factorized as the direct product of a Dirac algebra and another, called a ξ-algebra. The structure and representation of ξ-algebras are studied in detail. The factorization simplifies calculations with particles of spin > ½, because the ξ-algebra contains only one-sixteenth as many elements as the original matrix algebra.

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