Dirac Solitons in General Relativity and Conformal Gravity
Lead Research Organisation:
University of St Andrews
Department Name: Physics and Astronomy
Abstract
"Atom-like multi-fermion bound states in a deformable background: a case study in strong correlations"
Strongly correlated systems are a key area of study in modern physics [1]. These are systems that cannot be described, in any basis, as a weakly interacting set of quasi-independent degrees of freedom: i.e. their physics is intrinsically nonlinear. The formation of bound states is a paradigmatic route to excitations that are not perturbatively related to their constituent particles, and the most interesting cases are where there is back-action between the particles forming the bound state and the fields causing the binding in the first place [2].
In 1999, a particularly interesting case of such bound states was discovered [3]. These are formed from neutral fermions confined by gravity-like interactions in a deformable medium. The original work on this problem assumed that the interaction between the fermions and the medium was of Einsteinian form. However, the long-range nature of the strain fields in condensed matter analogues of such deformable media suggests that it might be equally relevant to explore such problems where the interaction between the fermions is mediated by conformal gravity [4].
In this project, we propose a thorough exploration of bound-state solutions for N fermions in a deformable medium described by conformal gravity. Specific questions include the following: What boundary conditions are mathematically sensible? What boundary conditions are physically appropriate for condensed-matter realisations of these models? What is the appropriate notion of mass for such bound states? What is the spectrum of N-fermion spherically symmetric states? Can the calculation be generalised to states that violate spherical symmetry, and if so, how?
[1] J. Quintanilla and C. Hooley, Physics World 22 (06), 32 (2009).
[2] P.W. Anderson, Phys. Rev. Lett. 64, 1839 (1990).
[3] F. Finster, J. Smoller, and S.-T. Yau, Phys. Rev. D 59, 104020 (1999).
[4] S.L. Adler, Rev. Mod. Phys. 54, 729 (1982).
Strongly correlated systems are a key area of study in modern physics [1]. These are systems that cannot be described, in any basis, as a weakly interacting set of quasi-independent degrees of freedom: i.e. their physics is intrinsically nonlinear. The formation of bound states is a paradigmatic route to excitations that are not perturbatively related to their constituent particles, and the most interesting cases are where there is back-action between the particles forming the bound state and the fields causing the binding in the first place [2].
In 1999, a particularly interesting case of such bound states was discovered [3]. These are formed from neutral fermions confined by gravity-like interactions in a deformable medium. The original work on this problem assumed that the interaction between the fermions and the medium was of Einsteinian form. However, the long-range nature of the strain fields in condensed matter analogues of such deformable media suggests that it might be equally relevant to explore such problems where the interaction between the fermions is mediated by conformal gravity [4].
In this project, we propose a thorough exploration of bound-state solutions for N fermions in a deformable medium described by conformal gravity. Specific questions include the following: What boundary conditions are mathematically sensible? What boundary conditions are physically appropriate for condensed-matter realisations of these models? What is the appropriate notion of mass for such bound states? What is the spectrum of N-fermion spherically symmetric states? Can the calculation be generalised to states that violate spherical symmetry, and if so, how?
[1] J. Quintanilla and C. Hooley, Physics World 22 (06), 32 (2009).
[2] P.W. Anderson, Phys. Rev. Lett. 64, 1839 (1990).
[3] F. Finster, J. Smoller, and S.-T. Yau, Phys. Rev. D 59, 104020 (1999).
[4] S.L. Adler, Rev. Mod. Phys. 54, 729 (1982).
Organisations
Publications
Leith P
(2020)
Fermion self-trapping in the optical geometry of Einstein-Dirac solitons
in Physical Review D
Leith P
(2021)
Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons
in Physical Review D
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R513337/1 | 01/10/2018 | 30/09/2023 | |||
| 2093516 | Studentship | EP/R513337/1 | 01/10/2018 | 31/03/2022 | Peter Leith |
| Description | The funded project involved research into hypothetical objects known as 'Dirac solitons', which can be loosely described as quantum states that are spatially localised via gravitational interactions. The majority of the research involved studying the properties of these and extending the theoretical framework to include additional forces and novel types of solutions. The three main achievements can be summarised as follows: (1) A rigorous analysis of many-particle Dirac solitons, which included the discovery of a 'self-trapping' effect, where the quantum wavefunction associated with a Dirac soliton becomes trapped around regions of highly-distorted space-time, resulting in an effective splitting of the wavefunction. (2) The extension of the framework to include a Higgs mechanism, and the discovery and analysis of soliton-like states in that context. It was found that the inclusion of the Higgs mechanism allows particles of much larger mass to form soliton-like states. (3) The discovery of new classes of soliton-like states that contain a central space-time singularity, the properties of which prove highly unusual, for example being gravitationally repulsive despite containing particles of positive mass. |
| Exploitation Route | The research is mainly academic in nature, and as such the outcomes are primarily useful to those working on research in the area of gravitationally localised quantum states. There are aspects, however, that may prove of wider significance to the more general physics community, in furthering progress in general relativity, and providing avenues via which the quantum gravity problem can be addressed. |
| Sectors | Other |