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Using Dirac notation, we can write It is easy to show that loop states are normalizable. Following tradition, we denote with also a multiloop, namely a collection of (possibly overlapping) loops , and we call a multiloop state. (Multi-)loop states represented the main tool for loop quantum gravity before the discovery of the spin network basis. Equation (19) can be explicitly written as an integral transform, as we will see in section 6. Associate an irreducible representation of SU(2) to each link of .

IndexGreat experiments of physicsReference Rohlf, Sec 8. . Electron spin Electron Spin Spin "up" and "down" allows two electrons for each set of spatial quantum numbers. In the pattern of other quantized angular momenta, this gives total angular momentum The resulting fine structure which is observed corresponds to two possibilities for the z-component of the angular momentum. One was the closely spaced splitting of the hydrogen spectral lines, called fine structure.

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