Anderson's absolute objects and constant timelike vector hidden in Dirac matrices.

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 117526, Russia
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December 17, 2001


Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices
are the only absolute objects of the Dirac equation. There are two ways of the Dirac matrices transformation: (1) Dirac matrices form a 4-vector and wave function  is a scalar, (2) Dirac matrices  are scalars and the wave function  is a spinor. In the first case the Dirac equation is nonrelativistic, in the second one it is relativistic. Transforming Dirac equation to another scalar--vector variables, one shows that the first way of transformation is valid, and the Dirac equation is not relativistic

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