arXiv subjects

Tobias Starke

Publications and source records attributed to Tobias Starke.

2 recordsLinked to original sources

arXiv2026

Quantenlogische Systeme und Tensorproduktraeume

In this work we present an intuitive construction of the quantum logical axiomatic system provided by George Mackey. The goal of this work is a detailed discussion of the results from the paper 'Physical justification for using the tensor product to describe two quantum systems as one joint system' [1] published by Diederik Aerts and Ingrid Daubechies. This means that we want to show how certain composed physical systems from classical and quantum mechanics should be described logically. To reach this goal, we will, like in [1], discuss a special class of axiomatically defined composed physical systems. With the help of certain results from lattice and c-morphism theory (see [2] and [23]), we will present a detailed proof of the statement, that in the quantum mechanical case, a composed physical system must be described via a tensor product space.

quant-ph↗

arXiv2026

Stationaere Kurven auf endlichdimensionalen Mannigfaltigkeiten

In this work we discuss the notion of stationary curves of the length functional, the so-called (weak) geodesics, on a Riemannian manifold. The motivation behind this work is to give a detailed description of many key concepts from differential geometry that one needs in order to understand the important notion of a (weak) geodesic. For this, we mainly focus on finite-dimensional smooth manifolds, so that we can develop an intuitive and geometric understanding of the concepts that we want to discuss. At the end of this work, we also provide a rough description of how one can generalise these ideas into infinite dimensions and how one can use (weak) geodesics in special algorithms for image matching (see [21]).

math.DG↗