Structures of quantum space-time

Many attempts to unify gravitational physics with other fundamental forces have pursued the idea of extending four-dimensional space-time to higher dimensions. Beginning with the introduction of the Kaluza–Klein theory of gauge potentials, such extensions have typically been carried out by increasing the spatial dimension of the space-time, while retaining the special role played by time. In methodologies of this sort it cannot be said that quantum mechanical characteristics of the fundamental forces are adequately incorporated into the structure of the higher dimensional space-time. Nor can it be said that the space-time is being treated in any useful sense as a quantum entity. If the universe is intrinsically quantum mechanical in an appropriate sense, then the most natural extension of space-time into higher dimensions has a completely different character from that suggested by the Kaluza–Klein theory and its generalizations.

In quantum mechanics, the dimensionality of the Hilbert space is directly related to the dimensionality of the corresponding space of Hermitian operators. Thus, if quantum theory is to be unified with space-time physics, it is natural to extend the space of matrices representing space-time points to higher dimensions, and hence to assume that the dimensionality of space-time is larger than four, perhaps infinite. A higher-dimensional extension of space-time in this manner is also consistent with the philosophy often put forward that spinors are just as fundamental as space-time points.

This line of thinking is motivated by the idea that the symmetries of space-time and the symmetries of quantum theory are, at the deeper level, indistinguishable. This generalized ‘equivalence principle’ reflects the notion that the fundamental symmetries or approximate symmetries we observe in nature should have a common origin, and that the breakdown of these symmetries should also have a common cause. In view of the generalized equivalence principle, one can postulate that space-time events are themselves infinite-dimensional Hermitian matrices. The model that results from such a construction is known as a quantum space-time model. 

The objective of the project is to investigate properties of quantum space-time, with some focus on (i) cosmological aspects (e.g., role of cosmological constants in symmetry breaking); and (ii) quantum aspects (role of entanglement, lack of commutativity, etc.) of the theory. 

Applicants are expected to hold a good first class degree in an MMath, MPhys or MSc qualification, or a first class honours degree in mathematics, physical sciences or engineering.

Open to UK students only.

IELTS Academic: 6.5 or above (or equivalent) with 6.0 in each individual category.