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1

It goes the other way, actually. In the Lagrangian and Hamiltonian approaches to classical dynamics (on which the quantum theory is based), you learn about "generalized coordinates" or "degrees of freedom." Most often this is used to reduce the complexity of a problem. The canonical example is a clock pendulum, constrained to move in a plane. The motion ...

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Just because space is curved, it does not mean it is a subspace of a higher dimension. All space is curved, even euclidean space. Flatness is a relation between a curvature of some subspace and the space it is part of. There is the wonderful image of space expanding equally as one might blow up a balloon, but this image might be as easily explained by ...

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In principle, $\mathcal{N}$ gives you the number of supercharges in your theory. There are, however, cases with more than one irreducible (pseudo-)real spinor representations. If you have $N$ charges in one and $N'$ charges in the other representation, you can denote the total number of charges as $\mathcal{N}=(N,N')$ in order to emphasize the difference. ...

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I am not sure that being in 3+1-D is a privilege. Actually, all the troubles with Feynmann integrals come from 4D. Secondly, the QFT is integrable only in 2+1-D. From the mathematical point of view, the 4D differentiable manifolds are most problematic. On contrary, I also heard that if the space is not 3D then the signal cannot be transmitted, but at the ...

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