Related papers: Matrix equations and trilinear commutation relatio…

Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…

The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…

Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces, because a fuzzy space is defined by a three-index coefficient of the product between functions on it, f_a*f_b=C_ab^cf_c. In this paper, this previous proposal is…

Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matrices and solving system of linear equations in a commutative…

We consider a matrix model depending on a parameter $\lambda$ which permits the fuzzy sphere as a classical background.By expanding the bosonic matrices around this background ones recovers a U(1) (U(n)) noncommutative gauge theory on the…

This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic…

In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…

We analyze two types of hermitian matrix models with asymmetric solutions. One type breaks the symmetry explicitly with an asymmetric quartic potential. We give the phase diagram of this model with two different phase transitions between…

We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by…

The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and…

We consider the (symmetric) Pascal matrix, in its finite and infinite versions, and prove the existence of symmetric tridiagonal matrices commuting with it by giving explicit expressions for these commuting matrices. This is achieved by…

In the previous study, we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various…

We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…

A parameterization of Grassmann-algebraic relations corresponding to the Pachner move 3--3 is proposed. In these relations, each 4-simplex is assigned a Grassmann weight depending on five anticommuting variables associated with its 3-faces.…

We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…

We consider certain examples of applications of the general methods, based on geometry and integrability of matrix models, described in hep-th/0601212. In particular, the nonlinear differential equations, satisfied by quasiclassical…

This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…

We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…

The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of…

We prove that the following statements are equivalent: a linear matrix equation with parameters forming a commuting set of diagonalizable matrices is consistent, a certain matrix constructed with the Drazin inverse is a solution of this…