Dynamical symmetries of semi-linear Schrödinger and diffusion equations

Stoimenov, Stoimen; Henkel, Malte

doi:10.1016/j.nuclphysb.2005.06.017

Cited by 28 publications

(43 citation statements)

References 68 publications

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“…The two-point function of the operator dual to φ computed from (4.10) coincides with the result of [3,4,[127][128][129]. We remark that the Ansatz for the boundary fields [3,4] is not necessary to derive (4.10).…”

Section: Non-relativistic Reductionsupporting

confidence: 76%

Nonrelativistic Holography — A Group-Theoretical Perspective

Dobrev

2014

Int. J. Mod. Phys. A

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We give a review of some group-theoretical results related to non-relativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant w.r.t. Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semi-simple Lie groups and adapted to the non-semisimple Schrödinger algebra. These requires development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed.

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Section: Non-relativistic Reductionsupporting

confidence: 76%

Nonrelativistic Holography — A Group-Theoretical Perspective

Dobrev

2014

Int. J. Mod. Phys. A

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“…This kind of approach would be analogous to the one used for finding dynamical symmetries of non-linear Schrödinger equations, see e.g. [2,16]. We hope to return to this elsewhere.…”

Section: Discussionmentioning

confidence: 98%

From Conformal Invariance towards Dynamical Symmetries of the Collisionless Boltzmann Equation

Stoimenov

Henkel

2015

Symmetry

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Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the 2D conformal algebra. In the case without external forces, the symmetry of the conformally-invariant transport equation is first generalized by considering the particle momentum as an independent variable. This new conformal representation can be further extended to include an external force. The construction and possible physical applications are outlined.

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“…This relation allows us to write a(h,k (r) +ǫ r+1 ) as a linear combination of the coefficients a(s,k (j) ), for all possible s and for j ≤ r. For instance, setting r = 0, the relation (19) reads as follows…”

Section: Lemmamentioning

confidence: 99%

Highest Weight Representations and Kac Determinants for a Class of Conformal Galilei Algebras With Central Extension

2012

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We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness and then deducing irreducibility of the associated highest weight quotient modules. A resulting classification of infinite dimensional irreducible modules is presented. It is also shown that a formula for the Kac determinant is deduced from our construction of singular vectors. Thus we prove a conjecture of Dobrev, Doebner and Mrugalla for the case of the Schrödinger algebra.

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Dynamical symmetries of semi-linear Schrödinger and diffusion equations

Cited by 28 publications

References 68 publications

Nonrelativistic Holography — A Group-Theoretical Perspective

Nonrelativistic Holography — A Group-Theoretical Perspective

From Conformal Invariance towards Dynamical Symmetries of the Collisionless Boltzmann Equation

Highest Weight Representations and Kac Determinants for a Class of Conformal Galilei Algebras With Central Extension

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