相关论文: Explicit BCJ numerators of nonlinear sigma model

We perform the covariant operator quantization of the spin-$1$ model in $2+1$ spacetime dimensions to rigorously establish its dualities. For this purpose, the Kugo-Ojima-Nakanishi formalism, based on an indefinite metric Hilbert space in…

We prove the bivariate Cayley-Hamilton theorem, a powerful generalization of the classical Cayley-Hamilton theorem. The bivariate Cayley-Hamilton theorem has three direct corollaries that are usually proved independently: The classical…

We study CKT (or bi-HKT) N = 4 supersymmetric quantum mechanical sigma models. They are characterized by the usual and the mirror sectors displaying each HKT geometry. When the metric involves isometries, a Hamiltonian reduction is…

A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that $0s$ in a qubit string do not contribute to the value of a number. They serve only as place…

Jacobi operators appear as kinetic operators of several classes of noncommutative field theories (NCFT) considered recently. This paper deals with the case of bounded Jacobi operators. A set of tools mainly issued from operator and spectral…

A binary linear code is called {\em LCD} if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on…

We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincar\'e-Einstein metrics and renormalized volume coefficients. As special cases, we find…

Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize…

This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively nonlinear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilizes the moment chain approach, where the…

We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…

We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a…

We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit…

Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact…

In this paper, the formal derivative operator defined with respect to context-free grammars is used to prove some properties about binomial coefficients and multifactorial numbers. In addition, we extend the formal derivative operator to…

Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of…

The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…

The kinematic algebra of Yang-Mills theory can be understood in the framework of homotopy algebras: the $L_{\infty}$ algebra of Yang-Mills theory is the tensor product of the color Lie algebra and a kinematic space that carries a…

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the…

This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only…

Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills…