# Tag Info

### Why radial quantization gives different spectrum?

TL;DR: The spectrum is discrete (continuous) since space is a compact circle $\mathbb{S}^1$ (non-compact line $\mathbb{R}^1$), respectively, cf e.g. this Phys.SE post. In more details: The radially ...
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### Planar spin in two-dimensional CFT

You should have one question per post. Here is the answer: $h_1+{\bar h}_1 = h_2 + {\bar h}_2$ is just one of the conditions. Lorentz invariance implies that the spin of the two fields must also be ...
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### Why radial quantization gives different spectrum?

I guess I’ve figure out what’s going on, the notion of translation is different (translation on cylinder is rotation and dilation on plane), so we are working with different momentum operators in this ...
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The main point is that the sum in OP's eq. (1) is only (absolutely) convergent if $|y|>|z|$, i.e. if OP's LHS $$\hat{T}(y)\hat{T}(z)~=~{\cal R}[\hat{T}(y)\hat{T}(z)]$$ is radially ordered. (...