Abstract
We give a complete description of symmetric and phase invariant states on spin systems and construct explicitly the corresponding G.N.S. representations. We establish a correspondence between, on one hand, these states and their ergodic decomposition and, on the other hand, a class of unitary representations of E(2)×ℝ and their decomposition in U.I.R. We interpret the thermodynamic limit a contraction of representations of U(2) to representations of E(2)×ℝ.
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Arnal, D., Cortet, J.C. A group theoretical approach of thermodynamic limits in spin systems. Lett Math Phys 1, 505–512 (1977). https://doi.org/10.1007/BF00399743
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DOI: https://doi.org/10.1007/BF00399743