相关论文: Cubic Matrix, Generalized Spin Algebra and Uncerta…
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer Duffin equations for particles of…
We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and…
Extends previous work on block-partitioned mixed generalized inverses from two subsets of system variables with distinct consistency requirements to three subsets. Does not include any notable theoretical contributions.
A simple cubic matrix model is presented, which has truncations that, it is argued, lead at the classical level to a variety of theories of gauge fields and gravity. These include Chern-Simons theory in d=3, and BF theory and general…
The retrodiction of spin measurements along a set of different axes is revisited in detail. The problem is presented in two different pictures, a geometric and a general algebraic one. Explicit measurement operators that allow the…
Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by…
A generalized twistor transform for spinning particles in 3+1 dimensions is constructed that beautifully unifies many types of spinning systems by mapping them to the same twistor, thus predicting an infinite set of duality relations among…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
The coupling of spin-3 gauge fields to three-dimensional Maxwell and $AdS$-Lorentz gravity theories is presented. After showing how the usual spin-3 extensions of the $AdS$ and the Poincar\'e algebras in three dimensions can be obtained as…
We derive the general form for a three-dimensional scale-invariant field theory with N=6 supersymmetry, SU(4) R-symmetry and a U(1) global symmetry. The results can be written in terms of a 3-algebra in which the triple product is not…
We consider the Heisenberg spin triangle with general coupling coefficients and general spin quantum number $s$. The corresponding classical system is completely integrable. In the quantum case the eigenvalue problem can be reduced to that…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…
We study 3d theories determined by three-manifolds. Previously, we found that some basic 3d dualities relate to the surgeries of three-manifolds and defined gauge circles and matter circles. In this note, we discuss some operations…
We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions. We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. We focus on generalizations of cluster algebras and…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…