# TLS - pseudospin or spin of $SU(2)$?


- usually, TLS is thought to be a parametrization/representation by PSEUDOspin

- if pseudospin is actual spin, then the particle with such a spin is a fermion

https://en.wikipedia.org/wiki/Spin-1/2
https://physics.stackexchange.com/questions/150590/spin-operators-commutation

- fixed-in-space spins

[spin operators on different sites commuting](https://users.ox.ac.uk/~phys1116/msm3.pdf)

## a paradox - a spin of a particle knows what statistics of two indistinguishable particles (two-particle wavefunction) canmust be

spin is a property of a single particle, q-statistics&indistinguishability is a property of two particles.
Yet the paradox is that **property of two particles/statistics is the consequence of the property of one particle⏎**
⏎
On the other hand, https://en.wikipedia.org/wiki/Quantum_entanglement underlines that an independent spin does not exist for q-entangled two-particles wavefunction. Spin-half is even more special because https://en.wikipedia.org/wiki/Orientation_entanglement makes it entangled under normal $2\pi$ rotations.

[Gibbs paradox for LEEs in glasses?](https://knowen.org/nodes/29090)

## http://www.bourbaphy.fr/frohlich.pdf

https://www.pas.rochester.edu/assets/pdf/undergraduate/su-2s_double_covering_of_so-3.pdf

# Parents

* QSNS - smoking guns - P