Bulg. J. Phys. vol.44 no.1 (2017), pp. 039-047

Boundedness of Two-Point Correlators Covariant under the Meta-Conformal Algebra

S. Stoimenov1, M. Henkel2,3
1Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria
2Rechnergestützte Physik der Werkstoffe, Institut für Baustoffe (IfB), ETH Zürich, Stefano-Franscini-Platz 3, CH - 8093 Zürich, Switzerland
3Groupe de Physique Statistique, Département de Physique de la Matiére et des Matériaux, Institut Jean Lamour (CNRS UMR 7198), France
Abstract. Covariant two-point functions are derived from Ward identities. For several extensions of dynamical scaling, notably Schr\"odinger-invariance, conformal Galilei invariance or meta-conformal invariance, the results become unbounded for large time- or space-separations. Standard ortho-conformal invariance does not have this problem. An algebraic procedure is presented which corrects this difficulty for meta-conformal invariance in (1+1) dimensions. A canonical interpretation of meta-conformally covariant two-point functions as correlators follows. Galilei-conformal correlators can be obtained from meta-conformal invariance through a simple contraction. All these two-point functions are bounded at large separations, for sufficiently positive values of the scaling exponents.

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