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unification_of_spacetime_symmetries:topological_field_theories

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unification_of_spacetime_symmetries:topological_field_theories [2019/02/09 09:19] 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