The weak nuclear force is one of the four fundamental forces of nature, alongside gravity, electromagnetism, and the strong nuclear force. It is responsible for certain types of radioactive decays and interactions involving particles known as W and Z bosons. The mathematical description of the weak nuclear force is given by the electroweak theory, which unifies the weak force with electromagnetism.
The electroweak theory combines two theories: the electromagnetic theory, described by quantum electrodynamics (QED), and the weak nuclear force theory, described by the Glashow-Weinberg-Salam (GWS) model. The equations of the electroweak theory involve a set of mathematical formalisms known as gauge theories.
One important aspect of the electroweak theory is the symmetry-breaking mechanism, which generates the masses of the W and Z bosons while leaving the photon massless. The symmetry-breaking is achieved through the Higgs mechanism, which introduces the Higgs field and the associated Higgs boson.
The full mathematical equations describing the electroweak theory are quite complex and involve the principles of quantum field theory. They go beyond the scope of a simple equation that can be written down concisely. The mathematical formalism involves a Lagrangian density that incorporates the gauge fields, matter fields, and interaction terms.
To summarize, while the weak nuclear force is part of the electroweak theory, its full mathematical description requires the framework of quantum field theory and gauge theories. The equations involved are highly complex and involve a Lagrangian density that encompasses the interactions between particles and fields.