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advanced_tools:group_theory:quotient_group

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advanced_tools:group_theory:quotient_group [2017/12/17 12:01]
jakobadmin
advanced_tools:group_theory:quotient_group [2018/05/15 04:58] (current)
jakobadmin ↷ Links adapted because of a move operation
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 <tabbox Why is it interesting?> ​ <tabbox Why is it interesting?> ​
  
-Quotient groups are crucial to understand, for example, [[advanced_notions:​symmetry_breaking|symmetry breaking]]. When a [[advanced_tools:​group_theory|group]] $G$ breaks to a [[advanced_tools:​group_theory:​subgroup|subgroup]] $H$ the resulting [[advanced_notions:​symmetry_breaking:​goldstones_theorem|Goldstone bosons]] live in the quotient space: $G/H$.+Quotient groups are crucial to understand, for example, [[advanced_notions:​symmetry_breaking|symmetry breaking]]. When a [[advanced_tools:​group_theory|group]] $G$ breaks to a [[advanced_tools:​group_theory:​subgroup|subgroup]] $H$ the resulting [[theorems:​goldstones_theorem|Goldstone bosons]] live in the quotient space: $G/H$.
  
 Moreover, quotient groups are a powerful way to understand geometry. Instead of a long list of axioms one can study geometry by treating the corresponding space as a homogeneous space (= coset space) and then study invariants of transformation groups of this homogeneous space. Moreover, quotient groups are a powerful way to understand geometry. Instead of a long list of axioms one can study geometry by treating the corresponding space as a homogeneous space (= coset space) and then study invariants of transformation groups of this homogeneous space.
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 --> Goldstone Bosons# --> Goldstone Bosons#
  
-The famous [[advanced_notions:​symmetry_breaking:​goldstones_theorem|Goldstone bosons]] that appear through the process of spontaneous [[advanced_notions:​symmetry_breaking|symmetry breaking]] of a group $G$ to some subgroup $H$ live in the coset space $G/H$.+The famous [[theorems:​goldstones_theorem|Goldstone bosons]] that appear through the process of spontaneous [[advanced_notions:​symmetry_breaking|symmetry breaking]] of a group $G$ to some subgroup $H$ live in the coset space $G/H$.
  
 This can be understood by considering an explicit example: This can be understood by considering an explicit example:
advanced_tools/group_theory/quotient_group.txt · Last modified: 2018/05/15 04:58 by jakobadmin