Related papers: Chiral Structures Under the Standard of Orthogonal…
Chiral perturbation theory is a very general expansion method which can be applied to any dynamical system which has continuous global symmetries and in which the ground state breaks some of these spontaneously. In these lectures we explain…
The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to…
Orthogonal Graph Representations are essential tools for testing existence of hidden variables in quantum theory. As required by the interpretation of Copenhaghe on the foundations of quantum mechanics, a physical observable is not…
In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…
The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations…
Molecular chirality leads to a wonderful variety of equilibrium structures, from the simple cholesteric phase to the twist-grain-boundary phases, and it is responsible for interesting and technologically important materials like…
The construction of algebraic structure of central molecular chirality is provided starting from the empirical Fischer projections for tetrahedrons. A matrix representation is given and the algebra of O(4) orthogonal group for rotations and…
The phase space of a particle on a group manifold can be split in left and right sectors, in close analogy with the chiral sectors in Wess Zumino Witten models. We perform a classical analysis of the sectors, and the geometric quantization…
We introduce a notion of chirality for generic quantum states. A chiral state is defined as a state which cannot be transformed into its complex conjugate in a local product basis using local unitary operations. We introduce a number of…
A formulation of abelian and non-abelian chiral gauge theories is presented together with arguments for the unitarity and renormalisability in four dimensions. IASSNS-HEP-94/70, UM-P-94/96, and RCHEP-94/26.
We study the chiral rings in N=2 and N=4 superconformal algebras. The chiral primary states of N=2 superconformal algebras realized over hermitian triple systems are given. Their coset spaces G/H are hermitian symmetric which can be compact…
Chirality is considered by many scientists to be mainly a geometric concept. There exists also a physical aspect of chirality which is largely being overlooked at. Two examples of mechanical devices are introduced here that represent…
Second-order equations of motion on a group manifold that appear in a large class of so-called chiral theories are presented. These equations are presented and explicitely solved for cases of semi-simple, finite-dimensional Lie groups. With…
The similarity transformations of quantum orthogonal groups are developed and FRT theory is reformulated to the Cartesian basis. The quantum orthogonal Cayley-Klein groups are introduced as the algebra functions over an associative algebra…
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…
Four-dimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly…
Chiral quantum optics is a growing field of research where light-matter interactions become asymmetrically dependent on momentum and spin, offering novel control over photonic and electronic degrees of freedom. Recently, the platforms for…
The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular on various aspects of the…
We construct a chiral theory of gravity in 7 and 8 dimensions, which are equivalent to Einstein-Cartan theory using less variables. In these dimensions, we can construct such higher dimensional chiral gravity because of the existence of…
An orthoset (also called an orthogonality space) is a set $X$ equipped with a symmetric and irreflexive binary relation $\perp$, called the orthogonality relation. In quantum physics, orthosets play a central role. In fact, a Hilbert space…