What he worked on was a way for elementary particles in the Standard Model of particle physics to get masses, the
Higgs mechanism
Peter Higgs was far from alone in working on this mechanism, and he, a group of Robert Brout and François Englert, and a group of Gerald Guralnik, C. R. Hagen, and Tom Kibble separately published papers on this mechanism almost simultaneously back in 1964.
Here are some alternative names:
- Brout–Englert–Higgs - BEH
- Higgs–Kibble - HK
- Englert–Brout–Higgs–Guralnik–Hagen–Kibble - EBHGHK
- Anderson–Higgs - AH
- Anderson–Higgs–Kibble - AHK
- Anderson-Brout-Englert-Guralnik-Hagen-Higgs-Kibble-'t-Hooft - ABEGHHKtH
What is the difficulty? Let us start with electromagnetism. It has two fields, the electric and the magnetic fields, and they both are made from two potentials, a scalar one and a vector one, related like time and space, and like energy and momentum. If one adds to this set of potentials a gradient of some arbitrary quantity, then the fields will remain unchanged. This is a "gauge symmetry".
If one gives a photonlike particle a mass in a naive way, that will break the gauge symmetry. But PH and his numerous colleagues discovered a way of keeping that breaking from happening: a Higgs particle, a particle that will preserve that symmetry, though in hidden form.
But it gives a mass to that photonlike particle by always having a nonzero ground-state or vacuum value. So in a sense, the Higgs particle is everywhere, giving mass to most other Standard-Model particles in proportion to how much those particles interact with it, complete with no interaction giving no mass.
It gets a nonzero ground state by having a potential with a hump in the middle, for zero field value. The ground state is for the field being in a trough around that hump, the trough's shape being involved with hiding that gauge symmetry.