Generalised definitions of certain functions and their uses

连续变量量子理论的广义上下文性可通过单次投影测量揭示

Generalised contextuality of continuous variable quantum theory can be revealed with a single projective measurement

本文提出了一种适用于连续变量系统的广义上下文性定义，通过构造可交换的测量族揭示量子理论的上下文性，并讨论了其与无广播的联系及无限维纠缠破裂通道的结构结果。

An embedding potential definition of channel functions

We show that the imaginary part of the embedding potential, a generalised logarithmic derivative, defined over the interface between an electrical lead and some conductor, has orthogonal eigenfunctions which define conduction channels into and out of the lead. In the case of an infinitely extended interface we establish the relationship between these eigenfunctions and the Bloch states evaluated over the interface. Using the new channel functions, a well-known result for the total transmission through the conductor system is simply derived.

Recursive Local Fractional Derivative

The definition of the local fractional derivative has been generalised to the orders beyond the critical order. This makes it possible to retain more terms in the local fractional Taylor expansion leading to better approximation. This also extends the validity of the product rule.

Dirichlet branes and a cohomological definition of time flow

Dirichlet branes are objects whose transverse coordinates in space are matrix-valued functions. This leads to considering a matrix algebra or, more generally, a Lie algebra, as the classical phase space of a certain dynamics where the multiplication of coordinates, being given by matrix multiplication, is nonabelian. Further quantising this dynamics by means of a star-product introduces noncommutativity (besides nonabelianity) as a quantum h-deformation. The algebra of functions on a standard Poisson manifold is replaced with the universal enveloping algebra of the given Lie algebra. We define…

可分解格林-双曲算子的Hadard状态

Hadamard states for decomposable Green-hyperbolic operators

本文提出了一种适用于可分解格林-双曲算子的广义Hadamard状态定义，并展示了其在量子场论中的应用和性质。

积分的几何定义及其应用

A Geometric Definition of the Integral and Applications

本文提出了一种基于三角剖分的积分定义，适用于李括形、随机积分和量子场论等场景，证明了余弦上同调与de Rham上同调的乘积相等。