Thursday, August 28, 2014

quantum field theory - Differential geometry of Lie groups



In Weinberg's Classical Solutions of Quantum Field Theory, he states whilst introducing homotopy that groups, such as $SU(2)$, may be endowed with the structure of a smooth manifold after which they may be interpreted as Lie groups. My questions are:



  • If we formulate a quantum field theory on a manifold which is also a Lie group, does that quantum field theory inherit any special or useful properties?

  • Does a choice of metric exist for any Lie group?

  • Are there alternative interpretations of the significance of Killing vectors if they preserve a metric on a manifold which is also a Lie group?




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