Quantum inequalities in integrable models and perturbative gravity in de Sitter space
Lead Research Organisation:
University of York
Department Name: Mathematics
Abstract
In this project the student will carry out research in one of the following two topics:
(1) It is well known that the energy density can become negative in quantum field theory. However, there are lower bounds on the negative energy density called quantum energy inequalities (QEIs). QEIs have been established mainly for linear field theories, but recently also for some self-interacting models, notably in integrable quantum field theories such as the massive Ising model. The student will investigate whether inequalities of this kind hold for a more general class of quantum observables in the massive Ising model, beyond the example of the energy density.
(2) QFT of massive scalar field theory in dS space has been shown to be equivalent to the Euclidean QFT on the sphere, which is much easier to analyse than the original Lorentzian theory. However, it is not known whether other important theories, such as Yang-Mills theory and perturbative gravity, in dS space can be formulated on the Euclidean sphere. The student will investigate the possibility of formulating perturbative gravity in dS space as a Euclidean theory on the sphere.
(1) It is well known that the energy density can become negative in quantum field theory. However, there are lower bounds on the negative energy density called quantum energy inequalities (QEIs). QEIs have been established mainly for linear field theories, but recently also for some self-interacting models, notably in integrable quantum field theories such as the massive Ising model. The student will investigate whether inequalities of this kind hold for a more general class of quantum observables in the massive Ising model, beyond the example of the energy density.
(2) QFT of massive scalar field theory in dS space has been shown to be equivalent to the Euclidean QFT on the sphere, which is much easier to analyse than the original Lorentzian theory. However, it is not known whether other important theories, such as Yang-Mills theory and perturbative gravity, in dS space can be formulated on the Euclidean sphere. The student will investigate the possibility of formulating perturbative gravity in dS space as a Euclidean theory on the sphere.
Organisations
People |
ORCID iD |
| Henning Bostelmann (Primary Supervisor) | |
| Lasse Schmieding (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509802/1 | 01/10/2016 | 31/03/2022 | |||
| 1945564 | Studentship | EP/N509802/1 | 01/10/2017 | 31/03/2021 | Lasse Schmieding |
| Description | If Pac-Man, who lives on a doughnut, studied the distribution of electric charges in his world, he would always find that the sum of all the charges in his space is exactly zero. This is a general result for the conserved charges of any model of the universe which has neither a spatial infinity nor a finite boundary, such as the surfaces of spheres or doughnuts. These methods have previously been applied by Brill, Deser, Moncrief and others to study classical and quantum gravitational systems, where the analogues of electric charge can be thought of as the total mass and momentum. The vanishing of the charges leads to quadratic constraints being imposed on the behaviour on the perturbations around a simple background, and there are well studied methods to deal with these constraints. As part of this award, similar methods were applied to a simple linearised supergravitational system on the surface of a three dimensional doughnut, where the graviton particle of gravity acquires a partner particle, the gravitino. The graviton and gravitino are connected by a supersymmetry transformation and there are conserved charges associated with this symmetry, the supercharges. On the doughnut, these supercharges also have to exactly vanish, and we generalised previously studied methods to be able to include the vanishing of the supercharges on the perturbations around a flat background. We constructed a space of states for the quantum system which obey all the linearisation constraints. |
| Exploitation Route | The group-averaging methods employed in the course of this award are used in the study of different models of quantum gravity, such as for loop quantum gravity. |
| Sectors | Other |
| URL | https://arxiv.org/abs/1912.12246 |