PT Invariant Complex E (8) Root Spaces

Fring, A. & Smith, M. (2011). PT Invariant Complex E (8) Root Spaces. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 50(4), pp. 974-981. doi: 10.1007/s10773-010-0542-8

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We provide a construction procedure for complex root spaces invariant under antilinear transformations, which may be applied to any Coxeter group. The procedure is based on the factorisation of a chosen element of the Coxeter group into two factors. Each of the factors constitutes an involution and may therefore be deformed in an antilinear fashion. Having the importance of the E(8)-Coxeter group in mind, such as underlying a particular perturbation of the Ising model and the fact that for it no solution could be found previously, we exemplify the procedure for this particular case. As a concrete application of this construction we propose new generalisations of Calogero-Moser Sutherland models and affine Toda field theories based on the invariant complex root spaces and deformed complex simple roots, respectively.

Item Type: Article
Additional Information: The original publication is available at
Uncontrolled Keywords: PI-symmetry, Non-Hermitian Hamiltonians, Perturbed Ising model, NON-HERMITIAN HAMILTONIANS, FIELD, SYMMETRY, CHAIN, MODEL
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science

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