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We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the…
Magnetic helicity is a fundamental quantity of magnetohydrodynamics that carries topological information about the magnetic field. By `topological information', we usually refer to the linkage of magnetic field lines. For domains that are…
We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space} and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformal submersion on a domain of Euclidean 3-space…
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible…
The electromagnetic field can be expressed in terms of two complex potentials $ \alpha, \beta ,$ which are related to the Debye potentials. The evolution equations for these potentials are derived, which are separable either in parabolic…
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the…
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant…
In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…
Studies of scattering amplitudes for electric and magnetic charges have identified previously overlooked multiparticle representations of the Poincar\'e group in four dimensions. Such representations associate nontrivial quantum numbers…
We give a simple and direct construction of a massless quantum field with arbitrary discrete helicity that satisfies Wightman axioms and the corresponding relativistic wave equation in the distributional sense. We underline the mathematical…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
The transfer of turbulent energy through an inertial range from the driving scale to dissipative scales in a kinetic plasma followed by the conversion of this energy into heat is a fundamental plasma physics process. A theoretical…
Helical magnetohydrodynamic turbulence with Hall effects is ubiquitous in heliophysics and plasma physics, such as star formation and solar activities, and its intrinsic mechanisms are still not clearly explained. Direct numerical…
Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves - as opposed to their…
Many-body Hilbert space is a functional vector space with the natural structure of an algebra, in which vector multiplication is ordinary multiplication of wave functions. This algebra is finite-dimensional, with exactly $N!^{d-1}$…
The principal series of unitary representations of the Lorentz group has been considered in the helicity basis. Decompositions of tensor products of the spinspaces are studied in the framework of projective representations of the symmetric…
We construct an infinite component relativistic wave equation which is a linear first order differential equation identical in form to a Dirac like equation, describing composite fields possessing multiple spin and energy states. The main…
In this paper we develop an existence theory for small amplitude, steady, two-dimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin--Helmholtz type discontinuity across the…