相关论文: Planons and their Carroll-Galilei symmetries
The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a…
We consider the quantum mechanics of an electron confined to move on an infinite cylinder in the presence of a uniform radial magnetic field. This problem is in certain ways very similar to the corresponding problem on the infinite plane.…
We study planar non-topological solitons in models with nonlinear potentials that are bounded from below. These models provide consistent completion for the classical consideration at any energy scale. The properties of our solutions…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…
The kinematics of particles refer to events and tangent vectors, while that of waves refer to dual gradient planes. Special relativity [1-3] applies to both objects alike. Here we show that spacetime exchange symmetry [7] implicit in the…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic'' central extension is introduced. It is used to describe non-relativistic anyons coupled to an electromagnetic field. Our…
We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer…
We use group theoretic methods to obtain the extended Lie point symmetries of the equations of motion for a charged particle in the field of a monopole. Cases with certain model magnetic fields and potentials are also studied. Our analysis…
The Galilean group is the group of symmetries of Newtonian mechanics, with Lie a lgebra $\gal(n)$. We find algebraically independent generators for the center of the universal enveloping algebra of $\gal(n)$ using coadjoint orbits.
We study the coadjoint orbits of the noncentrally extended (1+1)-affine Galilei group and compute the relevant Wigner functions built on them explicitly. We consider the centrally extended (1+1)-Galilei group and study its coadjoint orbits…
Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By…
We give a combinatorial characterization of minimally rigid planar frameworks with orientation-preserving crystallographic symmetry, under the constraint of forced symmetry. The main theorems are proved by extending the methods of the first…
We analyse the conservative evolution of spinning compact binaries to second post-Newtonian (2PN) order accuracy, with leading order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. As a main result we derive a…
This note provides an intrinsic construction of the Carrollian superplane $\Pi \mathbb{S}\simeq \mathbb{R}^{2|4}$ as a supermanifold generalisation of the Carrollian plane. Moving away from the $c\rightarrow 0$ limit of relativistic…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
In this thesis, we construct and classify planar noncommutative phase spaces by the coadjoint orbit method on the anisotropic and absolute time kinematical groups. We show that noncommutative symplectic structures can be generated in the…
We propose that models with spacetime dipole symmetry are connected to Lorentz invariant models via the Carrollian limit. In this way, a recently proposed model with spacetime dipole symmetry was readily reproduced together with its…
We derive a formulation of molecular dynamics that generates only symmetric configurations. We implement it for all 2D planar and 3D space groups. An atlas of 2D Lennard-Jones crystals under all planar groups is created with symmetric…