In QED, electrically charged particles are coupled by an uncharged, massless vector boson called the photon. The former are described by means of a fermionic spinor field $$\psi$$, and the latter by a bosonic vector (gauge) field $$A$$. The classical Lagrangian is postulated to be $$\mathcal L=\bar\psi(i\not D-m)\psi+\frac{1}{4e^2}F^2$$ where $$D\equiv\partial-iA$$ is the so-called gauge covariant derivative and $$F\equiv \mathrm dA$$ is the so-called field strength tensor. The quantum Lagrangian requires several modifications, such as fixing the gauge and introducing renormalisation constants. Once this is done, one may read off from $$\mathcal L$$ the Feynman rules of the theory, which are enough to calculate any prediction to an arbitrary order in perturbation theory.
By adding three additional, massive vector bosons (the $$Z^0$$ and $$W^{\pm}$$) which couple to the weak hyper-charge ($$T_3 - q \ \sin^2 \theta_W$$ in which $$q$$ is electric charge and $$T_3$$ is the third component of the weak isospin), the theory can be extended to cover the weak nuclear force as well.