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In mathematical physics, the gamma matrices, {,,,} , also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra , .
Die Dirac-Matrizen (nach dem britischen Physiker Paul Dirac), auch Gamma-Matrizen genannt, sind vier Matrizen, die der Dirac-Algebra genügen. Sie treten in der Dirac-Gleichung auf.
In mathematical physics, the Dirac algebra is the Clifford algebra, (). This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin-1 / 2 particles with a matrix representation of the gamma matrices, which represent the generators of the algebra.
Indeed, the canonical Lorentz transformation of gamma matrices 0 = ( 1) S S 1; (5.19) where not only the vector index is transformed by 1, but also the spinor matrix is conjugated by the corresponding spinor transformation S.6 In analogy to the invariance of the Minkowski metric, 0= , the Dirac equation is invariant if the gamma matrices are ...
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NOTE: it is important to realise that the Dirac gamma matrices are not four-vectors - they are constant matrices which remain invariant under a Lorentz transformation.
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3. Dez. 2022 · The gamma matrices were invented by physicist Paul Dirac in his attempt to formulate a relativistic version quantum mechanics suitable for charac-terizing the electron. In this paper, I will focus only on the mathematical aspects of the Dirac algebra and how one uses the trace on the gamma matrices.
30. Mai 2024 · The Dirac matrices are a class of 4×4 matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as gamma matrices or Dirac gamma matrices.
