You can find all of the previous Quantum Colloquia recordings below.

Peter Bradshaw

Algebraic approaches to physics are an active and growing area of research. Such theories often capture properties of a physical system in a simple and intuitive way [1], and often can yield new insights into established phenomena [2]. Their study also often avoids the need for explicit matrix or analytical representations, providing an elementary, flexible, and extensible way to describe a system coordinate-free and isolated from unnecessary additional structure. As such, they offer deep insights into the essential foundations of physical phenomena. In this talk, we will discuss a new algebraic theory to describe the spin of arbitrary non-relativistic systems, as derived in [3]. These algebras are real and written in terms of, and entirely characterised by, the complete set of physically distinct observables of the system, offering a novel characterisation of spin based on its physical properties instead of eigenvalues. This construction is realised directly from the symmetries of Euclidean three-space without: dynamical notions like angular momentum and time; nor additional mathematical structure, such as complex numbers. This indicates that spin is more fundamentally related to geometry than dynamics; this connection will be made more concrete by realising the spin of a non-relativistic system within a natural non-commutative geometry of position operators, without the need for "internal" degrees of freedom, following [4].