So, the Higgs field, is a Quantum Field.

The standard model is a Quantum Field Theory, which by field, simply indicates that there's a value for every point in space, and moment in time, and the quantum, indicates that what is really being described by the field, are particles, which are quantum in nature.

Gauge symmetry was generalized in 1954 by C.N. Yang, and Mills, in what is called Yang-Mills theory, which found its application in QFT, specifically the Weak Force.

Oh, he's also regarded as the founder of Quantum Field Theory, and the mathematical notation he formalized, eponymously named, is ubiquitous in Physics and is integral to Quantum Computing.