  Gauge theories, while describing fundamental interactions in nature, also
emerge in a wide variety of physical systems. Abelian gauge fields have been
predicted and observed in a number of novel quantum many-body systems,
topological insulators, ultracold atoms and many others. However, the
non-abelian gauge field, while playing the most fundamental role in particle
physics, up to now has remained a purely theoretical construction in many-body
physics. In the present paper we report the first observation of a non-abelian
gauge field in a spin-orbit coupled quantum system. The gauge field manifests
itself in quantum magnetic oscillations of a hole doped two-dimensional (2D)
GaAs heterostructure. Transport measurements were performed in tilted magnetic
fields, where the effect of the emergent non-abelian gauge field was controlled
by the components of the magnetic field in the 2D plane.
