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Anton Galajinsky

Publications and source records attributed to Anton Galajinsky.

At least 19 recordsLinked to original sources
arXiv2026

Perfect fluid equations with nonrelativistic conformal symmetry: Exact solutions

The group-theoretic approach is used to construct exact solutions to perfect fluid equations invariant under the Schrodinger group, or the l-conformal Galilei group, or the Lifshitz group. In each respective case, the velocity vector field looks similar to the Bjorken flow. It is shown that one can reach an arbitrarily high density (and hence pressure) for a short period of time by adjusting the value of l and other free parameters available.

math-ph↗
arXiv2026

The Bohlin variant of the Eisenhart lift

Inspired by the Bohlin transformation relating the planar harmonic oscillator to the Kepler problem, a variant of the Eisenhart lift is studied, in which a Lagrangian conservative dynamical system with d degrees of freedom is embedded into timelike geodesics of a conformally flat metric on a (d+2)-dimensional space-time of the Lorentzian signature. The uplift is used to construct novel examples of conformally flat metrics admitting higher rank Killing tensors.

nlin.SI↗
arXiv2026

Remarks on Galilean electromagnetism

It is shown that equations describing the Galilean electromagnetism in the presence of sources hold invariant under the l-conformal Galilei group for an arbitrary (half)integer parameter l. The group contains transformations which link an inertial frame of reference to those moving with constant accelerations of order up to 2l-1, thus pointing at potential dynamical instability.

physics.class-ph↗
arXiv2025

Rational Ruijsenaars-Schneider model with cosmological constant

The Ruijsenaars-Schneider models are integrable dynamical realizations of the Poincare group in 1+1 dimensions, which reduce to the Calogero and Sutherland systems in the nonrelativistic limit. In this work, a possibility to construct a one-parameter deformation of the Ruijsenaars-Schneider models by uplifting the Poincare algebra in 1+1 dimensions to the anti de Sitter algebra is studied. It is shown that amendments including a cosmological constant are feasible for the rational variant, while the hyperbolic and trigonometric systems are ruled out by our analysis. The issue of integrability of the deformed rational model is discussed in some detail. A complete proof of integrability remains a challenge.

hep-th↗
arXiv2024

Remarks on integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models

Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems.

nlin.SI↗
arXiv2023

Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body system

An N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model is constructed and its integrability is established. In particular, three functionally independent Grassmann-odd constants of the motion are given and their algebraic resolvability is proven. The supersymmetric generalization is used to build a novel integrable isospin extension of the Ruijsenaars-Schneider three-body system.

nlin.SI↗
arXiv2023

Remarks on higher Schwarzians

The Schwarzian derivative has recently received renewed attention in connection with the study of the Sachdev-Ye-Kitaev model. In mathematics literature, various higher order generalizations of the Schwarzian derivative are known due to Aharonov, Bertilsson, and Schippers. Physical applications of the higher Schwarzian derivatives have not yet been discussed in any detail. In this work, we link Bertilsson's variant to the l-conformal Galilei group, as well as discuss some of its interesting peculiarities. These include a recurrence relation, which allows one to construct the higher Schwarzians iteratively, a composition law, and symmetry transformations.

hep-th↗
arXiv2022

The group-theoretic approach to perfect fluid equations with conformal symmetry

The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal of this work is to discuss advantages and limitations of the method, which is here applied to construct perfect fluid equations with conformal symmetry. Four cases are studied in detail, which include the Schrodinger group, the l-conformal Galilei group, the Lifshitz group, and the relativistic conformal group.

hep-th↗
arXiv2022

Equations of fluid dynamics with the l-conformal Galilei symmetry

Equations of fluid dynamics are formulated, which hold invariant under the action of the l-conformal Galilei group. They include the conventional continuity equation, a higher order material derivative analogue of the Euler equation, and a suitable modification of the conventional equation of state. Conserved charges associated with the l-conformal Galilei symmetry transformations are presented.

hep-th↗
arXiv2022

Dynamical realizations of the Lifshitz group

Dynamical realizations of the Lifshitz group are studied within the group-theoretic framework. A generalization of the 1d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z. A similar generalization of the Ermakov-Milne-Pinney equation is proposed. Invariant derivative and field combinations are introduced, which enable one to construct a plethora of dynamical systems enjoying the Lifshitz symmetry. A metric of the Lorentzian signature in (d+2)-dimensional spacetime and the energy-momentum tensor are constructed, which lead to the generalized Ermakov-Milne-Pinney equation upon imposing the Einstein equations. The method of nonlinear realizations is used for building Lorentzian metrics with the Lifshitz isometry group. In particular, a (2d+2)-dimensional metric is constructed, which enjoys an extra invariance under the Galilei boosts.

hep-th↗
arXiv2022

Generalised point vortices on a plane

A three-vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three-vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It is shown that a generalised system, which is governed by a positive definite Hamiltonian, admits a natural integrable extension by spin degrees of freedom. It is emphasised that the n-vortex planar model and plenty of its generalisations enjoy the nonrelativistic scale invariance, which gives room for possible holographic applications.

hep-th↗
arXiv2021

Remarks on N=1 supersymmetric extension of the Euler top

A natural N=1 supersymmetric extension of the Euler top, which introduces exactly one fermionic counterpart for each bosonic degree of freedom, is considered. The equations of motion, their symmetries and integrals of motion are given. It is demonstrated that, although in general the system lacks the integrability property, it admits an interesting integrable reduction, for which all fermions are proportional to one and the same Grassmann-odd number - a value of the conserved supercharge. A generalisation involving an arbitrary three-dimensional real Lie algebra is proposed.

hep-th↗
arXiv2021

N=1,2,3 l-conformal Galilei superalgebras

The issue of constructing N=1,2,3 supersymmetric extensions of the l-conformal Galilei algebra is reconsidered following the approach in [JHEP 1709 (2017) 131]. Drawing a parallel between acceleration generators entering the superalgebra and irreducible supermultiplets of d=1, N-extended superconformal group, a new N=1 l-conformal Galilei superalgebra, two new N=2 variants, and two new N=3 versions are built. Realisations in terms of differential operators in superspace are given.

hep-th↗
arXiv2021

Some metrics admitting nonpolynomial first integrals of the geodesic equation

It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are constructed, each of which revealing a chain of generalised Killing vectors.

gr-qc↗
arXiv2021

Remarks on D(2,1;a) super-Schwarzian derivative

It was recently demonstrated that N=1,2,3,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realisations to finite-dimensional superconformal groups OSp(1|2), SU(1,1|1), OSp(3|2), SU(1,1|2), respectively, thus avoiding the use of superconformal field theory techniques. In this work, a similar construction is applied to the exceptional supergroup D(2,1;a), which describes the most general N=4 supersymmetric extension of SL(2,R), with the aim to study possible candidates for a D(2,1;a) super-Schwarzian derivative.

hep-th↗
arXiv2020

Spinning particles on 2-sphere in accord with the Bianchi classification

Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of spinning particles on 2-sphere, the spin degrees of freedom of which are represented by a 3-vector obeying the structure relations of a 3d real Lie algebra. Generalisations involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar extensions, which rely upon d=4,5,6 real Lie algebras, is elucidated.

hep-th↗
arXiv2020

N=3 super-Schwarzian from OSp(3|2) invariants

It was recently demonstrated that the N=0,1,2,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realizations to the finite-dimensional (super)conformal groups SL(2,R), OSp(1|2), SU(1,1|1), and SU(1,1|2), respectively. In this work, a similar scheme is realised for OSp(3|2). It is shown that the N=3 case exhibits a surprisingly richer structure of invariants, the N=3 super-Schwarzian being a particular member. We suggest that the extra invariants may prove useful in building an N=3 supersymmetric extension of the Sachdev-Ye-Kitaev model.

hep-th↗