Tom Lawrence

In my mathematical physics research, I study theories in which the usual four dimensions of spacetime are supplemented by extra spatial dimensions. These extra dimensions form a compact subspace of the full spacetime. I look at the action of transformations on fields on these spacetimes, and the symmetry groups to which these transformations belong. In particular, changes of coordinates on a higher-dimensional spacetime result in a field multiplet (representing some form of matter or geometric property of the spacetime) transforming under a symmetry group. However, the fact that the extra dimensions are compact means that the symmetry group is realised non-linearly. A field multiplet then carries a label describing its transformation properties in four-dimensional spacetime and a label describing its transformation properties in the compact subspace.

Gravity is viewed as a curvature in four-dimensional spacetime, while additional components of curvature describe non-gravitational interactions. This is therefore a geometric approach to unifying gravity with other fundamental interactions. I am interested in how different types of matter field can couple to these interactions, and how quantum and particle features can arise in such a theory. I am also looking at how quantities which are invariant under changes of coordinates can be used to distinguish between different topologies and geometries of the spacetime.

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I also run a sole trader consultancy, TRL Insight, carrying out research and analysis in relation to the UK public finances and local government policy. This focuses primarily on the funding and finance of English local government and its policy context, but also looks at other aspects of local government policy (both national policy and best practice within local government), and at public policy more widely. Much of this research and analysis is undertaken for particular contracts and commissioned outputs, but some is self-funded and occasionally self-published.

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