Related papers: Helicity invariants of force-free field for a rect…
Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic…
Given two Riemannian manifolds $(B,g_B)$ and $(F,g_F)$, we give harmonicity conditions for vector fields on the Riemannian warped product $B\times_fF$, with $f:B \longrightarrow ]0,+\infty[$, using a characteristic variational condition.…
A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a…
We study the possibility that primordial magnetic fields generated in the transition between inflation and reheating posses magnetic helicity, $H_M$. The fields are induced by stochastic currents of scalar charged particles created during…
It is shown that the second-order moment of helicity distribution (the Levich-Tsinober invariant of inviscid hydrodynamics) can be preserved as an adiabatic invariant in magnetohydrodynamics. The distributed chaos approach and inertial…
We use an analytic form for the Heisenberg-Euler Lagrangian to calculate the birefringent and dichroic properties of the vacuum for arbitrarily strong wrenchless fields. PACS : 12.20.Ds, 42.25.Lc 97.60.Jd, 98.70.Rz
A formal symplectic structure on RxM is constructed for the unsteady flow of an incompressible viscous fluid on a three dimensional domain M. The evolution equation for the helicity density is expressed via the divergence of the Liouville…
We propose the first covariant local action describing the propagation of a single free continuous-spin degree of freedom. The theory is simply formulated as a gauge theory in a "vector superspace", but can also be formulated in terms of a…
Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be…
We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The…
We present recent advancements in the computation of three-loop four-particle helicity amplitudes in full-color massless QCD. In this contribution, we focus on the $gg \to \gamma\gamma$ process. We show how to obtain compact analytic…
Classical gravitating field theories reduced to three dimensions admit manifest gauge invariances and hidden symmetries, which together make up the invariance group G of the theory. If this group is large enough, the target space is a…
The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are…
Magnetic helicity is robustly conserved in systems with very large magnetic Reynolds numbers, including most systems of astrophysical interest, and unlike kinetic and magnetic energy is not dissipated at small scales. This plays a major…
This paper is concerned with the helicity associated to solutions of the 3D incompressible Euler equations. We show that under mild conditions on the regularity of the velocity field of an incompressible ideal fluid it is possible to define…
We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale. In other words, the frame independence of such scale is built-in within those transformations, and one does not need to…
Dynamic equations that are the simplest conformally invariant generalization of Einstein equations with cosmological term are considered. Dimensions and Weyl weights of the additional geometrical fields (the vector and the antisymmetric…
In this paper we show that using frame-like gauge invariant formulation for the massive bosonic and fermionic fields in three dimensions the free Lagrangians for these fields can be rewritten in the explicitly gauge invariant form in terms…
Force-free magnetic fields are important in many astrophysical settings. Determining the properties of such force-free fields -- especially smoothness and stability properties -- is crucial to understanding many key phenomena in…
Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries, an imposed axial magnetic and electric field. The thus injected magnetic helicity in the system can be…