Australian National University mathematicians, Alan Carey and Adam Rennie, are in the forefront of the race to develop a powerful new system of geometry to apply to the strange realm of quantum mechanics.

Already, the system, non-commutative geometry, is showing promise in handling the theoretical framework of quantum physics. It can also describe the weird behaviour of `quantum states of matter', such as low temperature electrical conductors, at the centre of a worldwide research effort.

Carey, Rennie and colleagues are using the new geometry to refine quantum field theory, which extends quantum mechanics.

They recently caused a stir in the international mathematical community when they came up with a vast generalisation of the `local index formula', central to non-commutative geometry. Their approach unified and extended many of the discoveries made in the field since the 1960s.