Related papers: Two-Dimensional Space-Time Groups: Classification …
Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the…
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
Crystal generative models have shown rapid progress for accelerating the discovery of bulk, periodic materials. However, many material systems such as 2D superconductors, thin film semiconductors, and catalytic surfaces are diperiodic,…
We introduce the (2+1)-spacetimes with compact space of genus g and with r gravitating particles which arise by ``Minkowskian suspensions of flat or hyperbolic cone surfaces'', by ``distinguished deformations'' of hyperbolic suspensions and…
We introduce the time glass, a non-periodic analogue of the discrete time crystal that arises in periodically driven dissipative quantum many-body systems. This phase is defined by two key features: (i) spatial long-range order arising from…
A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
The spontaneous breaking of symmetries is a widespread phenomenon in physics. When time translational symmetry is spontaneously broken, an exotic nonequilibrium state of matter in which the same structures repeat themselves in time can…
Time crystals are systems that spontaneously break time-translation symmetry, exhibiting repeating patterns in time. Recent work has shown that non-Hermitian Floquet systems can host a time crystalline phase with quasi-long-range order. In…
In this paper, we consider the Poincare group (space time). In mathematics, the Poincar\'e group of spacetime, named after Henri Poincar\'e, is the group of isometries of Minkowski spacetime, introduced by Hermann Minkowski. It is a…
The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists…
This book introduces the new research area of Geometric Data Science, where data can represent any real objects through geometric measurements. The first part of the book focuses on finite point sets. The most important result is a complete…
Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation…
It is known that no length or time measurements are possible in sub-Planckian regions of spacetime. The Volovich hypothesis postulates that the micro-geometry of spacetime may therefore be assumed to be non-archimedean. In this letter, the…
It is shown that dynamics of D+2 elements of the (super)diffeomorphism group in one (1+1 for the super) dimension describes the D - dimensional (spinning) massless relativistic particles. The coordinates of this elements (D+2 einbeins, D+2…
Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under…
Euclidean geometry does not characterize dynamic electronic orbitals satisfactorily for even a single electron in a hydrogen atom is a formidable mathematical task with the Schrodinger equation. Here the author puts forward a new spacetime…
A choice of time-slicing in classical general relativity permits the construction of time-dependent wave functions in the ``frozen time'' Chern-Simons formulation of $(2+1)$-dimensional quantum gravity. Because of operator ordering…
We show the emergence of Floquet time crystal (FTC) phases in the Floquet dynamics of periodically driven $p$-spin models, which describe a collection of spin-1/2 particles with all-to-all $p$-body interactions. Given the mean-field nature…