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Schr"odinger invariance and space-time symmetries

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arxiv hep-th/0302187 v2 pith:OIQWCZOM submitted 2003-02-24 hep-th cond-matmath-phmath.MP

Malte Henkel , Jeremie Unterberger This is my paper · ORCID
classification hep-thcond-matmath-phmath.MP
keywords confequationodingerparabolicschrsymmetryalgebradynamic
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The free Schr\"odinger equation with mass M can be turned into a non-massive Klein-Gordon equation via Fourier transformation with respect to M. The kinematic symmetry algebra sch_d of the free d-dimensional Schr\"odinger equation with M fixed appears therefore naturally as a parabolic subalgebra of the complexified conformal algebra conf_d+2 in d+2 dimensions. The explicit classification of the parabolic subalgebras of conf_3 yields physically interesting dynamic symmetry algebras. This allows us to propose a new dynamic symmetry group relevant for the description of ageing far from thermal equilibrium, with a dynamical exponent z=2. The Ward identities resulting from the invariance under conf_d+2 and its parabolic subalgebras are derived and the corresponding free-field energy-momentum tensor is constructed. We also derive the scaling form and the causality conditions for the two- and three-point functions and their relationship with response functions in the context of Martin-Siggia-Rose theory.

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Cited by 5 Pith papers

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