Any of a number of quantum field theories put forward to explain fundamental interactions. A gauge theory involves a symmetry group (see group theory) for the fields and potentials (the gauge group). In the case of electrodynamics, the group is Abelian, whereas the gauge theories for the strong and weak interactions use non-Abelian groups. Non-Abelian gauge theories are sometimes known as Yang–Mills theories, although sometimes the term ‘Yang–Mills theory’ is reserved for the gauge group SU(2). This difference explains why quantum electrodynamics is a much simpler theory than quantum chromodynamics, which describes the strong interactions, and electroweak theory, which is the unified theory of the weak and electromagnetic interactions. In the case of quantum gravity, the gauge group is even more complicated than the gauge groups for either the strong or the weak interaction.

In gauge theories the interactions between particles can be explained by the exchange of particles (intermediate vector bosons, or gauge bosons), such as gluons, photons, and W and Z bosons.