Galilean invariance and magnetic monopoles

The existence of Dirac monopoles is shown to be incompatible with Galilean invariance. A discussion follows on the interpretation of monopoles physics in a Galilean approximation.     

Galilean invariance and magnetic charge

The Galilean and ‘dual’ invariant electrodynamics with magnetic charges is formulated. The definition of the main feature of relativistic electromagnetism is given. Consideration of different aspects of Galilean electromagnetism with magnetic charges is presented. It is shown in particular that the conclusion of Bacry & Kubar-Andre (1973) that the existence of the magnetic monopole is incompatible with Galilean invariance in general appears to be incorrect.     

Gauge functions and Galilean invariance of Lagrangians

A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance of the Lagrangian for Newton's law of inertia. It is suggested that this new solution of an old physics problem may have implications and potential applications to all gauge-based theories of physics.     

Entropy and Galilean invariance of lattice Boltzmann theories

A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube simulation.     

Relativity and lorentz invariance of entanglement distillability

We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can be achieved and all relevant cases presented.     

Investigation of Galilean invariance of multi-phase lattice Boltzmann methods

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is a major source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to two orders of magnitude for large velocities. We found that this is true in particular for methods in which the interactions are incorporated through a forcing term. Methods in which interactions are incorporated through a non-ideal pressure tensor only benefit for large velocities.     

Optimal dynamical characterization of entanglement

We show that, for experimentally relevant systems, there is an optimal measurement strategy to monitor the time evolution of entanglement under open system dynamics. This suggests an efficient, dynamical characterization of the entanglement of composite, open quantum systems.     

Weak-field approximation of effective gravitational theory with local Galilean invariance

We examine the weak-field approximation of locally Galilean invariant gravitational theories with general covariance in a (4+1)-dimensional Galilean framework. The additional degrees of freedom allow us to obtain Poisson, diffusion, and Schrödinger equations for the fluctuation field. An advantage of this approach over the usual (3+1)-dimensional General Relativity is that it allows us to choose an ansatz for the fluctuation field that can accommodate the field equations of the Lagrangian approach to MOdified Newtonian Dynamics (MOND) known as AQUAdratic Lagrangian (AQUAL). We investigate a wave solution for the Schrödinger equations.     

Environment-assisted invariance,entanglement, and probabilities in quantum physics

I introduce environment-assisted invariance or envariance-a symmetry exhibited by correlated quantum systems and related to causality-and describe how it can be used to understand the nature of ignorance and, hence, the origin and interpretation of Born's rule for quantum probabilities.     

Stokes-anti-Stokes entanglement in stimulated Raman scattering

A cavity model of Raman scattering from phonons by an undepleted laser field is considered. The fields in the interaction are coupled to the boson reservoir that produces the damping mechanism in the model. An analysis for the origination of quantum entanglement between the Stokes and anti-Stokes fields, depending on their coupling constants with the reservoir bosons and on the state of the reservoir, is performed under the assumption of the initial coherent state of phonons.     

Scale invariance rule in electromagnetic scattering

The volume integral equation formalism is used to prove the scale invariance rule for an arbitrarily sized scatterer with an arbitrary shape, morphology, and orientation. The only assumptions are that the scatterer is made of optically isotropic linear materials and is embedded in a homogeneous, linear, isotropic, and nonabsorbing infinite medium.     

Phenomenology of local scale invariance: from conformal invariance to dynamical scaling

Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z. For a given value of θ (or z), we construct local scale transformations, which can be viewed as scale transformations with a space–time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ, whereas the second type may describe dynamical scaling with a dynamical exponent z. Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ=1 and Schrödinger invariance for θ=2.The hypothesis of local scale invariance implies that two-point functions of quasiprimary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time autoresponse function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber–Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics.     

On the particle level of Galilean Quantum field theories

The procedure devised in a previous paper to obtain the exponential decay law for an unstable non-relativistic isolated particle within a Galilean Quantum Field Theory is applied to describe the transition from the particle to its decay products, as well as the transitions occurring in scattering processes.     

Applications of dynamical algebra of invariance of integrodifferential equations

General results on the algebraic properties of integrodifferential equations are used to obtain coherent and squeezed states and Green functions for the matrixdifferential models of condensed matter theory.     

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

D-dimensional massless particle with extended gauge invariance

We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk _N+a=k_N−a, k_2N =0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk _i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.