Related papers: Ambiguity theory, old and new
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
The antibracket formalism for gauge theories, at both the classical and quantum level, is reviewed. Gauge transformations and the associated gauge structure are analyzed in detail. The basic concepts involved in the antibracket formalism…
This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…
We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois…
We give a modern approach to the famous Cardano and Ferrari formulas in the algebraic equations with three and four degrees. Namely, we reconstruct these formulas from the point of view of superposition principle in quantum computation…
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the…
Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which…
This preprint is the extended version of a paper that will be published in the proceedings of the Oberwolfach conference "Explicit vs tacit knowledge in mathematics" (January 2012). It presents a case study on some algebraic researches at…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between…
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are:…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\theta$ ambiguity. We also discuss…
We present a Galois theory connecting finitary operations with pairs of finitary relations one of which is contained in the other. The Galois closed sets on both sides are characterised as locally closed subuniverses of the full iterative…
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
The fundamental concepts in the Galois Theory are separable, normal and Galois field extensions. These concepts are central in proofs of the Galois Theory. In the paper, we introduce a new approach, a ring theoretic approach, to the Galois…
We present here a spectrum of developments and predictions in gravitation theory in recent years which appear to be amongst some of the most exciting directions. These include the spacetime singularities, gravitational collapse final…
We develop a new connection between Differential Algebra and Geometric Invariant Theory, based on an anti-equivalence of categories between solution algebras associated to a linear differential equation (i.e. differential algebras generated…