FP6Индивидуална стипендия2004–2005

ADG IN QG · Applications of Abstract Differential Geometry to Quantum Gravity: a Sheaf and Category-Theoretic Approach

6РП — Действия „Мария Кюри“

Период: 2004-07-15 → 2005-07-14
Финансиране от ЕС: 40 000 €
Участници: 1
Схема: EIF

Линиите свързват координатора с партньорите.

Накратко на български

Абстрактната диференциална геометрия се прилага за описание на гравитацията чрез алгебрични структури, вместо чрез гладки пространства. Това помага за избягване на физическите безкрайности (сингулярности) в класическата гравитация и позволява формулирането на квантовата гравитация като теория на gauge-полетата.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Final Activity Report Summary - ADG IN QG (Applications of Abstract Differential Geometry to Quantum Gravity: a Sheaf and Category-Theoretic Approach)

An entirely algebraic, i.e. sheaf-theoretic, approach to gravity, both classical and quantum, was developed. With respect to classical gravity, we showed how the abstract differential geometry (ADG) technology could be applied, in a finitistic-algebraic setting, so as to completely avoid the singularities and their associated unphysical infinities assailing gravity (GR) due to the latters assumption of a smooth base space-time manifold, which was not present at all in ADG. With respect to quantum gravity (QG) we showed how ADG could be applied to formulate non-perturbative QG as a pure quantum gauge theory in a manifestly background independent way. In addition, during the course of development of our work, homological algebra, i.e. sheaf, category and topos-theoretic ideas were infused into more mainstream QG research channels, while we also made contact with other contemporary QG research trends, such as the application of ideas from the consistent histories approach to quantum mechanics, to quantum space and time structure, such as quantum space-time topology, and to gravity.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

The propesed mathematical physics research project is in the context of quantum gravity (QG). In view of the grave failure of classical differential geometric methods in attempts to quantize general relativity (GR) by retaining a smooth background geometr ical spacetime manifold, we shall take an alternative combinatory- algebraic route. The sought after QG has also been expected to shed more light on the problem of singularities and associated unphysical infinities assailing the pointed macroscopic spacet ime continuum of GR. Thus, to both ends, Mallios' Calculus and in extenso, base manifold-free, sheaf-theoretic Abstract Differential Geometry (ADG) will be applied to a finitistic-algebrainc scenario for quantum spacetime struture and dynamics that has be en recently proposed by this applicant in connection with sorkin's discrete causal set approach to Lorentzian QG. Also, again due to the inadequacy of the differential manifold model for spacetime at Planck scales, ma noncommutative topology, its sheaf the ory, and the concomitant organization of the resulting noncommutative sheaves' into a pointless quantum category or quantum topos suitable for addressing deep logico-geometrical issues in QG, will be developed.

Оригинален текст от CORDIS (на английски).

Участници

NATIONAL AND KAPODISTRIAN UNIVERSITY OF ATHENS · ATHENSКоординаторГърция

Връзки

Виж в CORDIS