A particular representation of gamma matrices

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Discussion Overview

The discussion revolves around the representation of gamma matrices in the context of Dirac spinors, specifically seeking a unitary equivalent representation where Dirac spinors with positive energy and generic momentum have only the first two components non-zero. The scope includes theoretical aspects of quantum mechanics and representations in particle physics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about a specific representation of gamma matrices that meets certain criteria for Dirac spinors.
  • Another participant suggests that many representations are unitarily equivalent to the standard representation and explains the concept of unitary equivalence.
  • A later reply clarifies the specific requirement regarding the components of the spinors in question.
  • Another participant proposes that the Foldy-Wouthuysen transformation might define the desired representation.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the specific representation sought, and while there is a suggestion that the Foldy-Wouthuysen transformation may apply, no consensus is reached on the exact representation or its implications.

Contextual Notes

The discussion does not resolve the mathematical details or assumptions underlying the representations of gamma matrices or the specific conditions for the 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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