Schrödinger invariance and spacetime symmetries

2003/02/24 by Malte Henkel, Jérémie Unterberger, Jeremie Unterberger · 1 voice · 8 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum chaos and dynamical systems #cond-mat #hep-th #math-ph

paper · pdf · doi:10.1016/s0550-3213(03)00252-9

openalex publication_date 2003/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 conf₃ 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.

Citations

• Infinite conformal symmetry in two-dimensional quantum field theory
• A new improved energy-momentum tensor

Cited by

• Schrödinger-invariance in the voter model
• On the Derivation of Equations of Motion from Symmetries in Quantum-Mechanical Systems via Heisenberg's Uncertainty
• Correlators in phase-ordering from Schrödinger-invariance
• A remarkable dynamical symmetry of the Landau problem
• Two-time autocorrelation function in phase-ordering kinetics from local scale invariance
• Perfect fluid equations with N=1,2 Schrodinger supersymmetry
• Critical ageing correlators from Schrödinger-invariance
• Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over the Twisted Schrödinger-Virasoro Lie algebra

Discussions

• I want to calculate the variation of the action of free Schrodinger field theory in $d$ dimensions under conformal rescaling. The transformations are given by: $$t\rightarrow{}t'=f(t)\text{ ,}\qquad x [stackexchange, 5 points]

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• Schrödinger symmetry: a historical review
• AGEING, DYNAMICAL SCALING AND CONFORMAL INVARIANCE
• Schrödinger-invariance in non-equilibrium critical dynamics
• Symmetries of the free Schrodinger Equation
• Free massless particles and extended space-time algebra