I am looking for a reference about a mathematical rigourous treatment of spin. I do not know if what I'm looking for actually exists, so let me get into details.

More precisely, I would like an exposition of spin starting from assumptions, or axioms (for example, of experimental nature) for the behavior of spin (not just $$\frac{1}{2}$$, but any $$m \in \frac{1}{2}\mathbb{N}$$) and then a detailed presentation of the model (observables and symmetries) and, if possible (and true), a proof that the model is unique (I am sure that this problem can be formulated as a problem of isomorphism of $$SU(2,\mathbb{C})$$ representations).

In other words, I would like to find something like this: "in such and such experiments, such thing is supposed to behave like that; we can model it by such Pauli matrices; Theorem: Any such representation is of the form this and this.".

• An edit has been made to another of my questions (physics.stackexchange.com/q/524171) saying that one shouldn't mix resource-recommendations with physics questions. This is why I post this in a separate question.
– Plop
Jan 13, 2020 at 9:10
• One assumes you have completely mastered the representation theory of su(2)? Jan 13, 2020 at 16:17
• Not necessarily; learning the math involved should only be a matter of time and careful reading; and if too difficult, I can take any mathematical statement as a hypothesis. It is just that as a mathematician, I encounter difficulties in reading physics texts.
– Plop
Jan 13, 2020 at 22:05
• Why did someone add the tag "fermions" ? $1 = \frac{1}{2}\cdot 2$, $2 \in \mathbb{N}$ and spin-$1$ particules are bosons, right?
– Plop
Jan 13, 2020 at 22:09
• Physicists usually (but not always) use the term "spin" for half-integral spin, and "angular momentum" for integral spin (which they knew about from SO(3), the rotational group of classical physics). See WP. Jan 13, 2020 at 23:15