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P. A. Horvathy

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

At least 73 records · Page 4Linked to original sources
arXiv2010

Exotic galilean symmetry and non-commutative mechanics

Some aspects of the "exotic" particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minimal as well as anomalous coupling to an external electromagnetic field is presented. Supersymmetric extension is also considered. Exotic Galilean symmetry is also found in Moyal field theory. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.

hep-th↗
arXiv2009

Non-relativistic conformal symmetries in fluid mechanics

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schroedinger group, which also involves, in addition, Schroedinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally-invariant relativistic theory, the recently discussed Conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.

physics.flu-dyn↗
arXiv2009

Monopole-charge instability

For monopoles with nonvanishing Higgs potential it is shown that with respect to "Brandt-Neri-Coleman type" variations (a) the stability problem reduces to that of a pure gauge theory on the two-sphere (b) each topological sector admits one, and only one, stable monopole charge, and (c) each unstable monopole admits $2\sum_{q<0} (2|q|-1)$ negative modes, where the sum goes over all negative eigenvalues $q$ of the non-Abelian charge $Q$. An explicit construction for (i) the unique stable charge (ii) the negative modes and (iii) the spectrum of the Hessian, on the 2-sphere, is then given. The relation to loops in the residual group is explained. The negative modes are tangent to suitable energy-reducing two-spheres. The general theory is illustrated for the little groups U(2), U(3), SU(3)/Z_3 and O(5).

hep-th↗
arXiv2009

The non-linear Schrödinger equation and the conformal properties of non-relativistic space-time

The cubic non-linear Schrödinger equation where the coefficient of the nonlinear term is a function $F(t,x)$ only passes the Painlevé test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.

math-ph↗
arXiv2009

Non-relativistic scattering of a spin-1/2 particle off a self-dual monopole

The non-relativistic scattering of a spin-1/2 particle off a self-dual monopole reduces, for large distances, to the dyon problem, studied previously by D'Hoker and Vinet. The S matrix (calculated by Zwanziger's algebraic method based on the o(3,1)\oplus o(3) dynamical symmetry, discovered by D'Hoker and Vinet) is shown to factorize into the product of the spinless S-matrix, S_0, with a spin-dependent factor. The total cross-section is identical to the one found in the spinless case.

hep-th↗
arXiv2009

Conserved quantities in non-abelian monopole fields

Van Holten's covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopole-like field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. It generalizes the fine-tuned inverse-square plus Coulomb potential, found before by McIntosh and Cisneros, and by Zwanziger, for a charged particle in the field of a Dirac monopole. Following Fehér, the result is interpreted as describing motion in the asymptotic field of a self-dual Prasad-Sommerfield monopole. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere and Wilczek, a conserved angular momentum is constructed, despite the non-conservation of the electric charge. No Runge-Lenz vector has been found.

hep-th↗
arXiv2008

The geometry of Schrödinger symmetry in non-relativistic CFT

The non-relativistic conformal "Schroedinger" symmetry of some gravity backgrounds proposed recently in the AdS/CFT context, is explained in the "Bargmann framework". The formalism incorporates the Equivalence Principle. Newton-Hooke conformal symmetries, which are analogs of those of Schroedinger in the presence of a negative cosmological constant, are discussed in a similar way. Further examples include topologically massive gravity with negative cosmological constant and the Madelung hydrodynamical description.

hep-th↗
arXiv2008

Non-Relativistic Conformal and Supersymmetries

Non-relativistic conformal (''Schrödinger'') symmetry is derived in a Kaluza-Klein type framework. Lightlike reduction of the massless Dirac equation from 5D Minkowski space yields Lévy-Leblond's non-relativistic equation for a spin 1/2 particle. Combining with the osp(1,1) SUSY found before provides us with a super-Schrödinger symmetry.

hep-th↗
arXiv2007

Lectures on (abelian) Chern-Simons vortices

Various aspects including the construction and the symmetries of Abelian Chern-Simons vortices are reviewed. Extended version of the Lectures delivered at NIKHEF (Amsterdam), July 2006. Typos corrected, some refernces added.

hep-th↗
arXiv2007

The Maslov correction in the semiclassical Feynman integral

The Maslov correction to the wave function is to the jump of $-π/2$ in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the geometry of paths, as conveniently explained in Feynman's path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used to illustrate the different derivations reviewed here.

quant-ph↗
arXiv2006

Non-commutative mechanics, in mathematical & in condensed matter physics

Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ``exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.

cond-mat.mes-hall↗
arXiv2006

Dynamics of semiclassical Bloch wave - packets

The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in presence of external fields using the method of the coadjoint orbit applied to the ``enlarged'' Galilei group.

cond-mat.mes-hall↗
arXiv2006

Anomalous Hall Effect in non-commutative mechanics

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in some ferromagnetic semiconductors while observing the anomalous Hall effect, we get a transverse shift, similar to that in the optical Hall effect.

cond-mat.mes-hall↗
arXiv2006

Fermat Principle for spinning light

Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields the semiclassical model used recently to derive the ``Optical Hall Effect'' (alias the ``Optical Magnus Effect'') for polarized light.

cond-mat.mes-hall↗
arXiv2006

Exotic galilean symmetry and non-commutative mechanics in mathematical & in condensed matter physics

The ``exotic'' particle model with non-commuting position coordinates, associated with the two-parameter central extension of the planar Galilei group, can be used to derive the ground states of the Fractional Quantum Hall Effect. The relation to other NC models is discussed. Anomalous coupling is presented. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.

hep-th↗
arXiv2006

Strings in plane-fronted gravitational waves

Brinkmann's plane-fronted gravitational waves with parallel rays --~shortly pp-waves~-- are shown to provide, under suitable conditions, exact string vacua at all orders of the sigma-model perturbation expansion.

hep-th↗
arXiv2006

Dynamal (super)symmetries of monopoles and vortices

The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, no smooth Runge-Lenz vector can exist; there is, however, a spectrum-generating conformal $o(2,1)$ dynamical symmetry that extends into $osp(1/1)$ or $osp(1/2)$ for spin 1/2 particles. Self-dual 't Hooft-Polyakov-type monopoles admit an $su(2/2)$ dynamical supersymmetry algebra, which allows us to reduce the fluctuation equation to the spin zero case. For large $r$ the system reduces to a Dirac monopole plus an suitable inverse-square potential considered before by McIntosh and Cisneros, and by Zwanziger in the spin 0 case, and to the `dyon' of D'Hoker and Vinet for spin 1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a `helicity-supersymmetry' analogous to the one Biedenharn found in the relativistic Kepler problem. Similar results hold for the Kaluza-Klein monopole of Gross-Perry-Sorkin. For the magnetic vortex, the N=2 supersymmetry of the Pauli Hamiltonian in a static magnetic field in the plane combines with the $o(2)\times o(2,1)$ bosonic symmetry into an $o(2)\times osp(1/2)$ dynamical superalgebra.

hep-th↗