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unification_of_spacetime_symmetries:topological_field_theories [2019/02/09 09:19]
jakobadmin [Why is it interesting?]
unification_of_spacetime_symmetries:topological_field_theories [2019/02/09 09:19] (current)
jakobadmin [Why is it interesting?]
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 "//a TQFT is a "​representation of a category,"​ that is, a functor from some category to a category of vector spaces (or Hilbert spaces). Thus, **the concept of symmetry in topological quantum field theories generalize that in earlier theories**. Earlier theories only dealt with group representations,​ while TQFTs are category representations!//"​ http://​math.ucr.edu/​home/​baez/​symmetries.html "//a TQFT is a "​representation of a category,"​ that is, a functor from some category to a category of vector spaces (or Hilbert spaces). Thus, **the concept of symmetry in topological quantum field theories generalize that in earlier theories**. Earlier theories only dealt with group representations,​ while TQFTs are category representations!//"​ http://​math.ucr.edu/​home/​baez/​symmetries.html
  
-"//The essential motivating idea behind topological ​?eld theories is that the modern physical ​the- +"//The essential motivating idea behind topological ​field theories is that the modern physical ​theories 
-ories are de?​ned ​in terms of invariance under certain group actions (e.g. gauge groups in particle +are defined ​in terms of invariance under certain group actions (e.g. gauge groups in particle 
-physics, diffeomorphism groups in general relativity, unitary operator groups in quantum ​mechan- +physics, diffeomorphism groups in general relativity, unitary operator groups in quantum ​mechanics). 
-ics).  Related to this is the idea that a system can be characterized by some number, an invariant +Related to this is the idea that a system can be characterized by some number, an invariant 
-under the group — for example, a four-vector in relativity or a vacuum expectation value in a +under the group — for example, a four-vector in relativity or a vacuum expectation value in a 
-?eld theory ​— or a “relative invariant” ​as seen in symmetry-breaking theories such as the Higgs +field theory ​— or a “relative invariant” ​as seen in symmetry-breaking theories such as the Higgs 
-mechanism. ​ In topological ​?eld theory, we are concerned with topological invariants, which are+mechanism. In topological ​field theory, we are concerned with topological invariants, which are
 objects computed from a topological space (usually a smooth manifold) without respect to any objects computed from a topological space (usually a smooth manifold) without respect to any
 metric [24]. Concretely, topological invariance means invariance under the diffeomorphism group metric [24]. Concretely, topological invariance means invariance under the diffeomorphism group
unification_of_spacetime_symmetries/topological_field_theories.txt · Last modified: 2019/02/09 09:19 by jakobadmin