Towards p-adic quantum bits and angular momentum theory via representations of the p-adic special orthogonal group SO(3)p

Developing the theme of p-adic quantum mechanics, where the configuration space is parametrised by p-adic numbers (for a fixed prime p), but wave-functions have the familiar complex amplitudes and Born's rule yields real-valued probabilities, we embark on the development of rotation symmetries of p-adic three- dimensional space, the compact group SO(3)_p and its representation theory as an approach to angular momentum in p-adic quantum mechanics, in particular p-adic spin and p-adic qubits. I will give an overview of the current state of the theory, starting from the description of SO(3)_p and its two-dimensional rotation subgroups, to the construction of the Haar measure, and of its first (simplest) two-dimensional complex unitary representations. Based on arXiv:2104.06228 and arXiv:2112.03362.