GEOMETRY QUANTUM · Quantum probability, geometry and gravity
6РП — Действия „Мария Кюри“
- Период
- 2004-06-01 → 2005-05-31
- Финансиране от ЕС
- 40 000 €
- Участници
- 1
- Схема
- ERG
Линиите свързват координатора с партньорите.
Накратко на български
Квантовите вероятности и тяхната връзка с геометрията се анализират чрез примери като времето за откриване на частица. Това помага за разработването на методи за описание на гравитацията и космологични модели.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - GEOMETRY QUANTUM (Quantum probability, geometry and gravity)
The project's aim was the theoretical study of probabilities in quantum theory, their relation to geometry and possible application in developing general quantisation techniques. The most important result of the research so far has been a detailed study of the probabilities associated to sequential quantum measurements. The mathematical description of these probabilities is very different from those of standard probability theory and possess many counter-intuitive features, as for example a very strong dependence on even tiny details of the measurement device. The reason is that the procedure of constructing these probabilities is not naturally obtained from the standard formalism of quantum theory--there are additional physical assumptions involved, which can in principle be experimentally tested. This work is related to the study of the so-called time-of-flight probabilities in quantum theory, namely the construction of a probability density for the time that a specific event took place, for example the detection of a particle. This is an old that is caused by the difficulty to include time as a physical observable in quantum theory. We show that the probabilities for the time of arrival are related to the probabilities of sequential measurements, a fact allowing us to construct an algorithm for the determination of the time-of-arrival probabilities for very general quantum systems. Other work within this project includes the use of geometrical methods (that appear naturally in the description of quantum 'measurements' at more than one moment of time) in the construction of the quantum mechanical description for a class of systems relevant to gravity (known as parameterised systems). We have elaborated in particular on the case of models relevant to cosmology.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
The main theme of the proposed research is the study of quantum probability and geometry and their relation. The longer term aim is to develop a quantisation scheme that will be employed in the context of quantum gravity. There are three main objectives to the proposed research. Firstly, in continuation of work in the previous Marie Curie grant, we will elaborate on the theory of quantum processes. This is a formalism of quantum theory, which was developed in analogy to stochastic processes but includes the information of the quantum interference phases. We will study quantum differential equations (the analogues of stochastic differential equations), systems in discrete time (which generalise quantum random walks) and the relation to quantum information geo metry. Secondly, we will elaborate on the relation of phase space geometry to quantum probability, which also was a major theme of the previous Marie Curie grant. We will study the second quantisation procedure using as our basic tool the coherent states o f the Poincare and apos; group and focus on the appearance of geometric phases, the geometric description of gauge interactions and the role ofspacetime symmetries. With the successful conclusion of these two objectives, we shall have fully established the geometric description for all known fundamental quantum systems, and we shall be able to develop a quantisation scheme based on quantum processes, which highlights the role of geometry, and consequently of the spacetime symmetries. Such a scheme will be a ble to deal rigorously with theories with non-trivial temporal structure. This will lead us to our third objective, which is the quantisation of models that are relevant for quantum gravity and are characterised by non-trivial temporal structure. We shall try to identify the basic principles of quantum growth processes, which are thought to implement the dynamics in the causal set description of gravity.
Оригинален текст от CORDIS (на английски).
Участници
- University of Patras · PATRASКоординаторГърция
Връзки
Данни: CORDIS, © Европейски съюз