diffeomorphism love

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from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A differentiable homeomorphism (with differentiable inverse) between differentiable manifolds.


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  • The Hamiltonian constraint NH = 0 defines a diffeomorphism structure on spatial manifolds by the lapse function N, but this is not identical to time.

    Einstein Still Rules, Says Fermi Telescope Team | Universe Today

  • The main problem for the latter is the general covariance of the field equations of General Relativity: any spacetime model and its image under a diffeomorphism (a infinitely differentiable, one-one and onto mapping of the model to itself) are in all observable respects equivalent to one another; all physical properties are expressed in terms of generally covariant relationships between geometrical objects.

    Structural Realism

  • Other: It's not nonperturbative quantization of diffeomorphism-invariant gauge theory.

    Slimbo-Poll: It's Not Rocket Science

  • For mathematical reasons not relevant here, it turns out to be possible to take a given model spacetime and perform a mathematical operation called a “hole diffeomorphism” h* on it; the diffeomorphism's effect is to shift around the matter content

    Causal Determinism

  • Figure 5: “Hole” diffeomorphism shifts contents of spacetime

    Causal Determinism

  • Maybe this is the resolution for the representation facts which you refer to from CFT, insofar as those facts perhaps pertain to continuous (projective) representations of the diffeomorphism group of the circle.

    Guest Post: Joe Polchinski on Science or Sociology?

  • Non-trivial unitary lowest-energy reps of diffeomorphism and gauge algebras are necessarily anomalous, and a quantized observer jumps right out of their representation theory.

    String Theory is Losing the Public Debate

  • As is well known already in 1D, interesting lowest-energy representations of the diffeomorphism algebra are necessarily anomalous (Virasoro algebra), and the higher-dimensional case is not different (multi-dimensional Virasoro algebra).

    String Theory is Losing the Public Debate

  • In AdS/CFT, not only the bulk spacetime but also the bulk diffeomorphism group are emergent: the CFT fields are completely invariant under the bulk diffeomorphisms (this is also what happens in the much more common phenomenon of emergent gauge symmetry).

    Guest Blogger: Joe Polchinski on the String Debates

  • Manifest diffeomorphism invariance seems too limited if we want to describe string theory.

    The String Theory Backlash


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