Sunday, 7 June 2020

special relativity - Vector spaces for the irreducible representations of the Lorentz Group


EDIT: The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain unanswered.


The definition of a representation is a map (a homomorphism) to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the



  • $(0,0)$ Representation

  • $(\frac{1}{2},0)$ Representation


  • $(0,\frac{1}{2})$ Representation





  • $(\frac{1}{2},0) \oplus (0,\frac{1}{2}) $ Representation




  • $(\frac{1}{2},\frac{1}{2})$ Representation



  • infinite dimensional Representation?




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