# Spin of a particle and spin quantum number [duplicate]

what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I do hope the + or - sign definitely talks about direction of spin! (kindly elaborate!)

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## marked as duplicate by dmckee♦Mar 1 '13 at 18:40

All particles have an internal degree of freedom which is intimately related to their behaviour under rotations. The state of this internal degree of freedom is an element of some Hilbert space $\mathcal{H}$. The spin $s$ of a particle determines the dimension of this vector space, and thus the number of simultaneously distinguishable (i.e. orthogonal) states available, given by $2s+1$.

Thus spin 0 has dimension 1 (a single state, so no dynamics), spin $\frac12$ has dimension 2 (an "up" and a "down" state once you fix a direction), spin 1 has dimension 3, and so on.

Particles also have a "magnetic" spin quantum number, usually denoted $m$, which identifies which way the particle is spinning. Once you fix a direction, the sign and magnitude of $m$ tell you the direction and size of the particle's angular momentum component on that axis.

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