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$X_i,Y_i,Z_i$ are three Pauli matrices acting on the $i$-th qubit where $i=1,2,3,4,5,6,7,8,9$ labels the qubit. In equation 4.1, the state is a superposition of tensor product of three states similar to $|000\rangle$. The latter is a state of three qubits, so if one takes the third power, it is a state of $3\times 3 = 9$ qubits. $X_1$ differs from $X_8$ by ...


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Good luck. To check the cancellation for particular groups like $E_8\times E_8$ and $SO(32)$, you will indeed have to get through similar group-theoretical tasks. Similar trace formula for the traces of $E_8$ transformations are especially yummy, including the factor of $1/30$. The orthogonal case is easier even if one is not an intimate friend of all ...


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See [1] M. Bos and V.P. Nair. Coherent State Quantization of Chern-Simons Theory. International Journal of Modern Physics A, A5:959, 1990. and chapter 20 of [2] V.P. Nair. Quantum Field Theory: A modern perspective. Springer, 2005. These references have geometric quantization of abelian Chern-Simons theory for $\Sigma=S^1 \times S^1$ (the first ref. ...


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So my question is, is Fourier Analysis essentially what String Theory is? Briefly, no. String theory "is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings." Fourier analysis "is the study of the way general functions may be represented or approximated by sums of ...


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Jerry Schirmer's answer to "Why are extra dimensions necessary?" seems (as far as I can tell) to give a good explanation of why compact dimensions are compact, from a QM point of view. I think it is more or less equivalent to the GR idea that mass/energy creates space and that the energy needed to create big space in higher dimensions is so much that it just ...


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The conformal compactification is supposed to belong to the projective space so we still identify points along the rays (equivalence classes under scaling) $$ (u,v,x_i)\sim \lambda (u,v,x_i), \quad \lambda \neq 0$$ Then there is the quadric equation you wrote down – an equation that respects the identification above – so both added variables $u,v$ are pretty ...


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In principle it should not. The problem with the Wick rotation is that what you are doing is embedding the Lorentzian manifold in a complex manifold of which it is a slice, and then looking for a different slice with Riemannian signature. In general there is no such Riemmanian slice, and even if it does exist it need not be unique. There is an old paper ...



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