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Register a new userNew BCH-like relations of the su(1, 1), su(2) and so(2, 1) Lie algebras
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Added by
Daniel Mart\\'inez Tibaduiza
Publication date
2020
fields
Physics
and research's language is
English
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In this work we demonstrate new BCH-like relations involving the generators of the su(1, 1), su(2) and so(2, 1) Lie algebras. We use our results to obtain in a straightforward way the composition of an arbitrary number of elements of the corresponding Lie groups. In order to make a self-consistent check of our results, as a first application we recover the non-trivial composition law of two arbitrary squeezing operators. As a second application, we show how our results can be used to compute the time evolution operator of physical systems described by time-dependent hamiltonians given by linear combinations of the generators of the aforementioned Lie algebras.
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Massless flows between the coset model su(2)_{k+1} otimes su(2)_k /su(2)_{2k+1} and the minimal model M_{k+2} are studied from the viewpoint of form factors. These flows include in particular the flow between the Tricritical Ising model and the Ising model. Form factors of the trace operator with an arbitrary number of particles are constructed, and numerical checks on the central charge are performed with four particles contribution. Large discrepancies with respect to the exact results are observed in most cases.
Massless flows from the coset model su(2)_k+1 otimes su(2)_k /su(2)_2k+1 to the minimal model M_k+2 are studied from the viewpoint of form factors. These flows include in particular the flow from the Tricritical Ising model to the Ising model. By analogy with the magnetization operator in the flow TIM -> IM, we construct all form factors of an operator that flows to Phi_1,2 in the IR. We make a numerical estimation of the difference of conformal weights between the UV and the IR thanks to the Delta-sum rule; the results are consistent with the conformal weight of the operator Phi_2,2 in the UV. By analogy with the energy operator in the flow TIM -> IM, we construct all form factors of an operator that flows to Phi_2,1. We propose to identify the operator in the UV with sigma_1Phi_1,2.
In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional nonlinear Schrodinger type equation introduced by Zakharov and studied later by Strachan. Interestingly our studies show that not all integrable higher dimensional systems admit Kac-Moody-Virasoro type sub-algebras. Particularly the two integrable systems mentioned above do not admit Virasoro type subalgebras, eventhough the other integrable higher dimensional systems do admit such algebras which we have also reviewed in the Appendix. Further, we bring out physically interesting solutions for special choices of the symmetry parameters in both the systems.
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