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Extension of KMS states and angular momentum

We present a description of β‐KMS equilibrium states with respect to some one‐parameter subgroup of (T×R3) ⧠K, over an asymptotically Abelian algebra of observables (here T×R3 is the group of time and space translations and K a compact group acting on R3). In the case where K=SO(3), the group of space rotations, we get a characterization of the angular momentum of such states as a parameter occurring in their description, similar to the chemical potential, and classify all of them according to their invariance group, a closed subgroup of T×R×SO(2).