Related papers: Finding the Standard Model of Particle Physics, A …
Recently Anishetty, Majumdar and Sharatchandra have proposed a way of characterizing topologically non-trivial configurations for 2+1-dimensional Yang-Mills theory in a local and manifestly gauge invariant manner. Here we develop criteria…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
We present a general formalism able to derive the kinetic equations of polymer dynamics. It is based on the application of nonequilibrium thermodynamics to analyze the irreversible processes taking place in the conformational space of the…
Applying symmetry reduction to a class of $\mathrm{SL}(2,\mathbb R)$-invariant third-order ODEs, we obtain Abel equations whose general solution can be parametrised by hypergeometric functions. Particular case of this construction provides…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
The simplest (2+1)-dimensional mechanical systems associated with light-like curves, already studied by Nersessian and Ramos, are reconsidered. The action is linear in the curvature of the particle path and the moduli spaces of solutions…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the…
We study the issue of description of spinning particle dynamics by means of recently proposed world sheet concept. A model of irreducible spinning particle in the $3d$ Minkowski space with two gauge symmetries is considered. The classical…
The Standard Model of particle physics can be deduced from a small number of axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra…
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation…
Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…
We propose a geometric explanation of the standard model of Glashow, Weinberg and Salam for the known elementary particles. Our model is a generic Quantum Field Theory in dimension four, obtained by developing along a Lorentz sub-manifold…
This article gives conjecturally correct algorithms to construct canonical bases of the irreducible polynomial representations and the matrix coordinate rings of the nonstandard quantum groups in GCT4 and GCT7, and canonical bases of the…
We propose a scalable encoding of combinatorial optimization problems with arbitrary connectivity, including higher-order terms, on arrays of trapped neutral atoms requiring only a global laser drive. Our approach relies on modular…
Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…