相关论文: Constructive Matrix Theory

In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…

Let $M_n$ denote the algebra of $n \times n$ complex matrices and let $\mathcal{A}\subseteq M_n$ be an arbitrary structural matrix algebra, i.e. a subalgebra of $M_n$ that contains all diagonal matrices. We consider injective maps $\phi :…

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian…

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Lof's type theory (hence…

On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Amp\`ere operator is defined. It is shown that it satisfies a…

A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…

We apply matrix methods to arithmetic functions by associating matrices to the functions in a manner drawn from the theory of symmetric functions. Then we study the characteristic polynomials of the associated matrices.

In this work we discuss the construction of "simplicial BF theory", the field theory with finite-dimensional space of fields, associated to a triangulated manifold, that is in a sense equivalent to topological BF theory on the manifold…

We construct a four dimensional topological Quantum Field Theory from a modular tensor category. We complete the proof in the case of SU(2)q at a root of unity. Our construction may be important in the physical interpretation of the Chern…

An inductive realization of Loop Vertex Expansion is proposed and is applied to the construction of the $\phi_1^4$ theory. It appears simpler and more natural than the standard one at least for some situations.

In this letter, we discuss certain universal predictions of the large charge expansion in conformal field theories with $U(1)$ symmetry, mainly focusing on four-dimensional theories. We show that, while in three dimensions quantum…

Structuring theories is one of the main approaches to reduce the combinatorial explosion associated with reasoning and exploring large theories. In the past we developed the notion of development graphs as a means to represent and maintain…

We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…

We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple…

We present a scenario for deriving Maxwell theory from IIB matrix model. Four dimensional spacetime and theories on it relate different dimensional ones by applying appropriate limits of the backgrounds of matrix model. It is understood by…

We extend the recursion formula for matrix Bessel functions, which we obtained previously, to superspace. It is sufficient to do this for the unitary orthosymplectic supergroup. By direct computations, we show that fairly explicit results…

We study four dimensional field theory from the low-energy effective theory of Type I, II or heterotic string theories. Chiral fermions in four dimensions are obtained by several mechanisms. Especially, the background flux is one of the…

A unitary matrix model is proposed as the large-N matrix formulation of M theory on flat space with toroidal topology. The model reproduces the motion of elementary D-particles on the compact space, and admits membrane states with nonzero…

In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the…

A partial description of the structure of positive unital maps $\phi: M_2(\bC) \to M_{n+1}(\bC)$ ($n\geq 2$) is given.