ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract This paper gives what is believed to be a new discussion of Dirac matrices and of the Dirac matrix description of Lorentz transformations. The five anticommuting quantities γ J (J=1, 2, 3, 0, 5) are treated on an equal footing and recognition of the rule for expressing the three-fold product γ J γ K γ L in terms of one- and two-fold products and of invariant “five-space” tensorsg J K , ε J K I P Q allows all kinds of multiplication and trace laws for Dirac matrices to be derived systematically. The “five-space” formalism for Dirac matrices affords a very convenient vehicle for the Dirac matrix description of de Sitter transformations of a space with quadratic formg K L xHxL. By considering the subset of these which leave the coordinatex 5 invariant, the Dirac matrix description of Lorentz transformations is obtained. Not only does this description give the well-known formula for any Lorentz transformation matrixL in terms of the matrixS, which enters the transformation law of a Dirac spinor ψ(x) underL, it also gives an explicit and apparently new inverse formula expressingS in terms ofL.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01773348
