Related papers: Interpretations and Representations of Classical T…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
The classical number system encodes magnitude using a single scalar value whose sign positive or negative has remained conceptually unchanged for centuries. This work introduces Multisign Algebra, a mathematical generalization of the sign…
We give a simple geometrical interpretation of classical $\W$-transformations as deformations of constant energy surfaces by canonical transformations on a two-dimensional phase space.
Magnetic translation groups are considered as central extensions of the translation group T=Z^n by the group of factors (a~gauge group) U(1). The obtained general formulae allow to consider a magnetic field as an~antisymmetric tensor (of…
This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and…
We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the Kraus operator on a single system. We begin with the…
Hermitian tensors are generalizations of Hermitian matrices, but they have very different properties. Every complex Hermitian tensor is a sum of complex Hermitian rank-1 tensors. However, this is not true for the real case. We study basic…
In this article we give two different ways of representations of circular words. Representations with tuples are intended as a compact notation, while representations with trees give a way to easily process all conjugates of a word. The…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes.…
This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments…
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality.…
We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors as pencils of matrices. We provide a complete…
This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable…
Tensor diagrams are a handy way to depict complicated relationships between objects in projective geometry. One of the simpler ones takes two copies of a $3\times 3$ matrix and computes its adjugate. In this paper, we give a geometric…
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
Music is an art, perceived in unique ways by every listener, coming from acoustic signals. In the meantime, standards as musical scores exist to describe it. Even if humans can make this transcription, it is costly in terms of time and…