# 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).

### 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 Edward Leith |