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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] Both sides previous revision Previous revision 2018/03/24 10:10 jakobadmin [FAQ] 2018/03/24 10:10 jakobadmin 2018/03/24 10:09 jakobadmin [Layman] 2018/03/24 10:09 jakobadmin [Student] 2018/03/24 10:08 jakobadmin [Why is it interesting?] 2018/03/24 10:08 jakobadmin [Why is it interesting?] 2018/03/24 10:05 jakobadmin [Layman] 2018/03/24 10:01 jakobadmin created 2018/03/24 10:10 jakobadmin [FAQ] 2018/03/24 10:10 jakobadmin 2018/03/24 10:09 jakobadmin [Layman] 2018/03/24 10:09 jakobadmin [Student] 2018/03/24 10:08 jakobadmin [Why is it interesting?] 2018/03/24 10:08 jakobadmin [Why is it interesting?] 2018/03/24 10:05 jakobadmin [Layman] 2018/03/24 10:01 jakobadmin created Line 104: Line 104: -->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. <-- <--