Searcharxiv⌕ Search

arXiv subjects

P. A. Horváthy

Publications and source records attributed to P. A. Horváthy.

At least 19 recordsLinked to original sources
arXiv2017

Conformal and projective symmetries in Newtonian cosmology

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schr{ö}dinger group or the Conformal Galilei Algebra.

gr-qc↗
arXiv2014

Anomalous Hall Effect for semiclassical chiral fermions

Semiclassical chiral fermions manifest the anomalous spin-Hall effect: when put into a pure electric field they suffer a side jump, analogous to what happens to their massive counterparts in non-commutative mechanics. The transverse shift is consistent with the conservation of the angular momentum. In a pure magnetic field instead, spiraling motion is found. Motion in Hall-type perpendicular electric and magnetic fields is also studied.

hep-th↗
arXiv2010

Dynamical supersymmetry of spin particle-magnetic field interaction

We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants associated with the system using a SUSY extension of a previously proposed algorithm, based on Grassmann-valued Killing tensors. Conserved quantities arise for certain definite values of the gyromagnetic factor: $\N=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous systems can be unified into an $\N=2$ SUSY system built by doubling the number of Grassmann variables. The planar system also exhibits an $\N=2$ supersymmetry without Grassmann variable doubling.

hep-th↗
arXiv2009

Bogomolny equations and conformal transformations in curved space

The coupling of the Higgs field through the Ricci tensor, put forward by Balakrishna and Wali, is derived using a conformal rescaling of the metric. Earlier results on "Bogomolny-type" equations in curved space, by Comtet, and others, are recovered. The procedure can be generalized to any static background metric.

hep-th↗
arXiv2009

Applications of chiral supersymmetry for spin fields in self-dual backgrounds

Due to chiral supersymmetry the (nonzero mode) spectral and symmetry properties of a 4-dimensional, self-dual Dirac-Yang-Mills operator $\D$ can be recovered from those of the corresponding scalar Laplacian $D^2$. It is shown that a similar result holds for higher spins, and that in the 4-vector case the super-symmetric partners are $-D^21_4$ and the fluctuation operator. The reduction to $D^2$ is used to simplify previous analyses of the (nonzero mode) spectrum of $\D$ and of the fluctuations for a BPS-monopole, and to explain the Kepler and su(2/2) (super)symmetries of a system studied recently by D'Hoker and Vinet.

hep-th↗
arXiv2003

Vortices in the Landau--Ginzburg Model of the Quantized Hall Effect

The `Landau--Ginzburg' theory of Girvin and MacDonald, modified by adding the natural magnetic term, is shown to admit stable topological as well as non-topological vortex solutions. The system is the commun $λ\to0$ limit of two slightly different non-relativistic Maxwell--Chern--Simons models of the type introduced recently by Manton. The equivalence with the model of Zhang, Hansson and Kivelson is demonstrated.

hep-th↗
arXiv2002

Chaplygin gas with field-dependent Poincare symmetry

The relativistic generalization of the Chaplygin gas, put forward by Jackiw and Polychronakos, is derived in Duval's Kaluza-Klein framework, using a universal quadratic Lagrangian. Our framework yields a simplified proof of the field-dependent Poincaré symmetry Our action is related to the usual Nambu-Goto action [world volume] of $d$-branes in the same way as the Polyakov and the Nambu action are in strings theory.

hep-th↗
arXiv2002

Non-commuting coordinates in vortex dynamics and in the Hall effect, related to "exotic" Galilean symmetry

Vortex dynamics in a thin superfluid ${}^4$He film as well as in a type II superconductor is described by the classical counterpart of the model advocated by Peierls, and used for deriving the ground states of the Fractional Quantum Hall Effect. The model has non-commuting coordinates, and is obtained by reduction from a particle associated with the ``exotic'' extension of the planar Galilei group.

hep-th↗
arXiv2001

Exotic galilean symmetry in the non-commutative plane, and the Hall effect

Quantum Mechanics in the non-commutative plane is shown to admit the ``exotic'' symmetry of the doubly-centrally-extended Galilei group. When coupled to a planar magnetic field whose strength is the inverse of the non-commutative parameter, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.

hep-th↗
arXiv2001

Exotic plasma as classical Hall Liquid

A non-relativistic plasma model endowed with an ``exotic'' structure associated with the two-parameter central extension of the planar Galilei group is constructed. Introducing a Chern-Simons statistical gauge field provides us with a self-consistent system; when the magnetic field takes a critical value determined by the extension parameters, the fluid becomes incompressible and moves collectively, according to the Hall law.

cond-mat.mes-hall↗
arXiv2000

Symmetries of fluid dynamics with polytropic exponent

The symmetries of the general Euler equations of fluid dynamics with polytropic exponent are determined using the Kaluza-Klein type framework of Duval et $\it{al}$. In the standard polytropic case the recent results of O'Raifeartaigh and Sreedhar are confirmed and generalized. Similar results are proved for polytropic exponent $γ=-1$, which corresponds to the dimensional reduction of $d$-branes. The relation between the duality transformation used in describing supernova explosion and Cosmology is explained.

hep-th↗
arXiv2000

Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.

hep-th↗
arXiv2000

Monopole supersymmetries and the Biedenharn operator

The hidden supersymmetry of the monopole found by De Jonghe et al. is generalized to a spin $\2$ particle in the combined field of a Dirac monopole plus a $λ^2/r^2$ potential [considered before by D'Hoker and Vinet], and related to the operator introduced by Biedenharn a long time ago in solving the Dirac-Coulomb problem. Explicit solutions are obtained by diagonalizing the Biedenharn operator

hep-th↗
arXiv2000

The exotic Galilei group and the "Peierls substitution"

Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not commute. Our model can be viewed as the non-relativistic counterpart of the relativistic anyon considered before by Jackiw and Nair. For a particle moving in a magnetic field perpendicular to the plane, the two parameters combine with the magnetic field to provide an effective mass. For vanishing effective mass the phase space admits a two-dimensional reduction, which represents the condensation to collective ``Hall'' motions and justifies the rule called ``Peierls substitution''. Quantization yields the wave functions proposed by Laughlin to describe the Fractional Quantum Hall Effect.

hep-th↗
arXiv1999

The symmetries of the Manton superconductivity model

The symmetries and conserved quantities of Manton's modified superconductivity model with non-relativistic Maxwell-Chern-Simons dynamics (also related to the Quantized Hall Effect) are obtained in the ``Kaluza-Klein type'' framework of Duval et al.

math-ph↗
arXiv1999

Field-dependent symmetries of a non-relativistic fluid model

As found by Bordemann and Hoppe and by Jevicki, a certain non-relativistic model of an irrotational and isentropic fluid, related to membranes and to partons, admits a Poincaré symmetry. Bazeia and Jackiw associate this dynamical symmetry to a novel type of ``field dependent'' action on space-time. The ``Kaluza-Klein type'' framework of Duval et al. is used to explain the origin of these symmetries and to derive the associated conserved quantities. In the non-interacting case, the symmetry extends to the entire conformal group.

math-ph↗
arXiv1999

Topology of non-topological Chern-Simons vortices

The quantized magnetic flux $Φ=-4πN\sk, N=0,\pm1,...$ of non-topological vortices in the non-relativistic Chern-Simons theory is related to the topological degree of the $S^2\to S^2$ mapping defined by lifting the problem to the Riemann spheres. Regular solutions with finite degree only arise for rational functions, whose topological degree, $N$, is the commun number of their zeros and poles on the Riemann sphere, also called their algebraic order.

hep-th↗