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arXiv · hep-th/0302187

Schr"odinger invariance and space-time symmetries

Malte Henkel·Jeremie Unterberger
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Abstract

The free Schrödinger 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 Schrödinger 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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Malte Henkel, Jeremie Unterberger. 2003-04-15. Schr"odinger invariance and space-time symmetries. https://doi.org/10.1016/s0550-3213(03)00252-9

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