Towards p-adic quantum bits via representations of the p-adic group of rotations SO(3)ₚ

We develop the p-adic quantum mechanics introduced by Volovich, where physics takes place in three-dimensional p-adic space rather than Euclidean space.
We study the p-adic rotation group SO(3)ₚ, and we outline a program to classify its continuous complex unitary projective representations.
These can be interpreted as a theory of p-adic angular momentum, where the p-adic qubit arises from those two-dimensional irreducible representations.
I will give an overview of this work, by describing the main features of SO(3)ₚ (in parallel to its real counterpart), by showing two approaches to its Haar measure
and by developing a method to find some simple two-dimensional representations. Based on arXiv:2104.06228 and arXiv:2112.03362.