A particular representation of gamma matrices

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SUMMARY

The discussion centers on the representation of gamma matrices that are unitarily equivalent to the standard representation, specifically focusing on Dirac spinors with positive energy and generic momentum. Participants confirm that any unitary matrix can be used to generate equivalent representations through the transformation A=UBU†. The Foldy-Wouthuysen transformation is identified as the method that ensures Dirac spinors exhibit non-zero values only in the first two components for positive energy and momentum.

PREREQUISITES
  • Understanding of gamma matrices in quantum mechanics
  • Familiarity with unitary transformations
  • Knowledge of Dirac spinors
  • Concept of the Foldy-Wouthuysen transformation
NEXT STEPS
  • Research the mathematical properties of unitary matrices
  • Study the Foldy-Wouthuysen transformation in detail
  • Explore applications of gamma matrices in quantum field theory
  • Learn about different representations of Dirac spinors
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Physicists, particularly those specializing in quantum mechanics and quantum field theory, as well as students seeking to deepen their understanding of gamma matrices and Dirac spinors.

array89
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I was wondering if there is a representation of gamma matrices unitarily equivalent to the standard representation for which Dirac Spinors with positiv energy and generic momentum have only the first two component different prom zero. Anyone can help me?
 
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array89 said:
I was wondering if there is a representation of gamma matrices unitarily equivalent to the standard representation...

yeah, presumably there are lots of representations which are unitarily equivalent to the standard representation... I'm not sure what you are asking? As far as I know unitary equivalence means a matrix A is related to another matrix B via A=UBU^\dagger where U is unitary. So take any unitary matrix U and apply U\gamma_\mu U^\dagger for each mu to generate an equivalent rep.
 
yes I know it. I was wondering what's the representation for which any spinor of positive energy and momentum p have only the first two component different from zero
 
Isn't that the definition of the Foldy Wouthuysen transformation?
 

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