Noah-Vaughan-Roberts-University-of-St-Andrews

LOCALISED STATES OF FERMIONS IN A SPACETIME OBEYING CONFORMAL GRAVITY By Noah Vaughan-Roberts, University of St Andrews School of Physics & Astronomy Supervised by Dr Chris Hooley & Pr

LOCALISED STATES

OF FERMIONS IN A SPACETIME OBEYING

CONFORMAL

GRAVITY

By Noah Vaughan-Roberts, University of St Andrews

School of Physics & Astronomy Supervised by Dr Chris Hooley & Prof Keith Horne

Problem investigated – Two neutral quantum particles (e.g neutrons) which are only interacting via conformal

gravity (an alternative to the theory proposed by Einstein via General Relativity)

Methodology:

Derive equations that need to be solved

Find the correct boundary conditions

Create a solver on a computer to solve the equations

Analyse solutions and find those which are valid

The Standard model of Particle physics explains with

incredible accuracy almost every effect in the

Universe, even so far as to predict the presence of

particles before we even find evidence for them (I.e

the Higgs boson) The one obvious aspect which we

all experience that the standard model doesn’t

incorporate is Gravity For the theorists hunting for

the almost mysticised ‘Theory of Everything’, finding

how gravity acts at the quantum level is of the upmost

importance

Findings: In the case of massless particles (or very low mass ones), the results were quite unexpected In the Einsteinian

gravity problem, the particles could exist at fixed energy levels (like the electron orbitals of an atom)

In the Conformal problem the curvature of spacetime itself allows for a continuous group of energies to be valid under the laws of quantum mechanics For any energy put into the equations, a unique real-world solution is retrieved (fig 3)

Fig 2 a (Left) shows the lowest allowed energy state (Ground state) Fig 2 b (Right) shows the second lowest energy state (1 st excited state) The Y axis is a representation of the curvature of spacetime, and the clean bumps are consistent with these being the real-world solutions.

Fig 3 A graph showing the relative strength between the quantum fields of the problem

For any given energy value the graph winds around to a certain end point Fig 3 a (Left) is at one value of energy, while 3 b (right) is at a higher value.