Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there exists an $(o)$-continuous state $\omega$ on $E$, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras

Motivations and Physical Aims of Algebraic QFT

We present illustrations which show the usefulness of algebraic QFT. In particular in low-dimensional QFT, when Lagrangian quantization does not exist or is useless (e.g. in chiral conformal theories), the algebraic method is beginning to reveal its strength.Comment: 40 pages of LateX, additional remarks resulting from conversations and mail contents, removal of typographical error

`Iconoclastic', Categorical Quantum Gravity

This is a two-part, `2-in-1' paper. In Part I, the introductory talk at `Glafka--2004: Iconoclastic Approaches to Quantum Gravity' international theoretical physics conference is presented in paper form (without references). In Part II, the more technical talk, originally titled ``Abstract Differential Geometric Excursion to Classical and Quantum Gravity'', is presented in paper form (with citations). The two parts are closely entwined, as Part I makes general motivating remarks for Part II.Comment: 34 pages, in paper form 2 talks given at ``Glafka--2004: Iconoclastic Approaches to Quantum Gravity'' international theoretical physics conference, Athens, Greece (summer 2004

Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)-continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras

String theory and the crisis of particle physics II or the ascent of metaphoric arguments

This is a completely reformulated presentation of a previous paper with the same title; this time with a much stronger emphasis on conceptual aspects of string theory and a detailed review of its already more than four decades lasting history within a broader context, including some little-known details. Although there have been several books and essays on the sociological impact and its philosophical implications, there is yet no serious attempt to scrutinize its claims about particle physics using the powerful conceptual arsenal of contemporary local quantum physics. I decided to leave the previous first version on the arXiv because it may be interesting to the reader to notice the change of viewpoint and the reason behind it. Other reasons for preventing my first version to go into print and to rewrite it in such a way that its content complies with my different actual viewpoint can be found at the end of the article. The central message, contained in sections 5 and 6, is that string theory is not what string theorists think and claim it is. The widespread acceptance of a theory whose interpretation has been obtained by metaphoric reasoning had a corroding influence on the rest of particle physics theory as will be illustrated in several concrete cases. The work is dedicated to the memory of Juergen Ehlers with whom I shared many critical ideas, but their formulation in this essay is fully within my responsibility.Comment: A dedication and an epilog to the memory of Juergen Ehlers. Extension of the the last two sections, removal of typos and changes in formulation, 68 pages late