Related papers: Chiral Structures Under the Standard of Orthogonal…
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more…
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
We describe a substructure for matter in which metric relations are not assumed as properties of a physical manifold, and instead the metric of general relativity is found in configurations of particle interactions. The 'state' of a…
Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian…
We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both…
We describe the singularities in the averaged density of states and the corresponding statistics of the energy levels in two- (2D) and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in…
The first papers on o-minimal structures appeared in the mid 1980s, since then the subject has grown into a wide ranging generalisation of semialgebraic, subanalytic and subpfaffian geometry. In these notes we try to show that this is in…
We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra…
The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…
On the example of exceptional families of viruses we i) show the existence of a completely new type of matter organization in nanoparticles, in which the regions with a chiral pentagonal quasicrystalline order of protein positions are…
Chiral-parity (parity-doublet) effective Lagrangian models provide a compact and symmetry-consistent framework for describing baryons and their negative-parity partners in terms of linearly-realized chiral symmetry. Unlike the conventional,…
The implications of chiral symmetry for the quark model are discussed. In particular its connection with the meson-baryon approach is outlined. It is stressed that in the closure approximation, where the intermediate baryon states are used…
The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincar\'{e} group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption…
We show that the recently observed chirality in the charge ordered phase of TiSe2 can be understood as a form of orbital ordering. The microscopic mechanism driving the transition between the novel chiral state and the non-chiral charge…
In beginning quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this article we will consider chiral symmetries which anticommute with the Hamiltonian.…
It is shown that a locally geometrical structure of arbitrarily curved Riemannian space is defined by a deformed group of its diffeomorphisms
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…
The aim of this work is an analysis of distal and non-distal behavior in dense pairs of o-minimal structures. A characterization of distal types is given through orthogonality to a generic type in $M^{\operatorname{eq}}$, non-distality is…
We develop a structural theory of chirality for inverse semigroups and show how it propagates canonically to \'{e}tale groupoids and twisted groupoid $C^*$-algebras. Starting from inverse semigroup data equipped with admissible twist…
Artificial nanostructures enable fine control of electromagnetic fields at the nanoscale, a possibility that has recently been extended to the interaction between polarised light and chiral matter. The theoretical description of such…