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The OSp(2|2)-invariant planar dynamics of a D=4 superparticle near the horizon of a large mass extreme black hole is described by an N=2 superconformal mechanics, with the SO(2) charge being the superparticle's angular momentum. The {\it…
In this paper, we explore the concept of $\sigma$-quasiconvexity for functions defined on normed vector spaces. This notion encompasses two important and well-established concepts: quasiconvexity and strong quasiconvexity. We start by…
If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this…
We generalize our holographic derivation of spontaneous angular momentum generation in 2 + 1 dimensions in several directions. We consider cases when a parity violating perturbation responsible for the angular momentum generation can be…
The Maxwell group in 2+1 dimensions is given by a particular extension of a semi-direct product. This mathematical structure provides a sound framework to study different generalizations of the Maxwell symmetry in three space-time…
Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping…
We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary space-times. These expressions involve non-locally defined conformal factors. In certain…
We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric…
We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant $\Lambda$. In…
We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or 1+1 dimensional field theories on the…
A two dimensional surface can be considered as three dimensional shell whose thickness is negligible in comparison with the dimension of the whole system. The quantum mechanics on surface can be first formulated in the bulk and the limit of…
We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski…
We construct one-particle states as unitary, irreducible representations of Poincare group in front form, characterized by a special null vector, dubbed reference vector. We demonstrate that this construction has massive-massless…
In condensed matter systems it is necessary to distinguish between the momentum of the constituents of the system and the pseudomomentum of quasiparticles. The same distinction is also valid for angular momentum and pseudoangular momentum.…
Infrared effects in the scattering of particles in gravity and electrodynamics entail an exchange of relativistic angular momentum between pairs of particles and the gauge field. Due to this exchange particles can carry an asymptotically…
We consider a description of membranes by (2,1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant systems, as well as…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
The Poincar\'e algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electro-magnetic backgrounds and possibly including the backreaction due the…
Starting from the coadjoint Poincar\'e algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincar\'e algebra is able to induce a mechanism of…
Asymptotic properties of classical field electrodynamics are considered. Special attention is paid to the long-range structure of the electromagnetic field. It is shown that conserved Poincare quantities may be expressed in terms of the…