2018/10/31 by Malte Henkel, Stoimen Stoimenov
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/ab3282
published as J. Stat. Mech. 084009 (2019) · 1+32 pages, 5 figures, dedicated to the memory of V. Rittenberg. Final form. (several extensions with respect to precursor article arXiv:1711.05062)
arxiv created 2019/07/10 · arxiv updated 2019/08/22
Meta-conformal transformations are constructed as sets of time-space transformations which are not angle-preserving but contain time- and space translations, time-space dilatations with dynamical exponent z=1 and whose Lie algebras contain conformal Lie algebras as sub-algebras. They act as dynamical symmetries of the linear transport equation in d spatial dimensions. For d=1 spatial dimensions, meta-conformal transformations constitute new representations of the conformal Lie algebras, while for d≠ 1 their algebraic structure is different. Infinite-dimensional Lie algebras of meta-conformal transformations are explicitly constructed for d=1 and d=2 and they are shown to be isomorphic to the direct sum of either two or three centre-less Virasoro algebras, respectively. The form of co-variant two-point correlators is derived. An application to the directed Glauber-Ising chain with spatially long-ranged initial conditions is described.