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advanced_tools:group_theory:desitter [2018/03/24 10:10]
jakobadmin
advanced_tools:group_theory:desitter [2018/03/24 10:10] (current)
jakobadmin [FAQ]
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 -->It ist confusing what a "​five-dimensional"​ group like $SO(4,1)$ has to say about our four-dimensional world. Does this mean deSitter theories predict a fifth dimension?# -->It ist confusing what a "​five-dimensional"​ group like $SO(4,1)$ has to say about our four-dimensional world. Does this mean deSitter theories predict a fifth dimension?#
  
-No, recall that an explicit representation of the [[the_standard_model:​poincare_group|Poincare group]] is given by $(5 \times 5)$ matrices, too! This is, because the Lorentz group transformations are $(4 \times 4)$ matrices themselves and in oredr to describe translations,​ we need to make these matrices into $(5 \times 5)$ matrices. See, for example, chapter 4 "The Poincaré transformations"​ in [[http://​www.springer.com/​us/​book/​9783642154812|Symmetries and Group Theory in Particle Physics]] by Costa and Fogly.+No, recall that an explicit representation of the Poincare group is given by $(5 \times 5)$ matrices, too! This is, because the Lorentz group transformations are $(4 \times 4)$ matrices themselves and in oredr to describe translations,​ we need to make these matrices into $(5 \times 5)$ matrices. See, for example, chapter 4 "The Poincaré transformations"​ in [[http://​www.springer.com/​us/​book/​9783642154812|Symmetries and Group Theory in Particle Physics]] by Costa and Fogly.
  
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advanced_tools/group_theory/desitter.txt · Last modified: 2018/03/24 10:10 by jakobadmin