The Standard Model of particle physics is arguably the most successful theory in the history of physics. It represents our best understanding of the entire subatomic world. The theory is encapsulated in a single equation, below, known as the Standard Model Lagrangian.
Left side of the equation is the Lagrangian.
The principle of least action says that
Nature will always try to follow the path that minimizes rate of change of a certain quantity called the action.
This tendency can be used to figure out how pretty much any physical process play out. The Lagrangian is the part of this action quantity that we work with. If we plug the Lagrangian of a system into the Euler-Lagrange equation and the result will be equations describing how that system will move and change over time.
Right part of the equation has several different terms that each accounts for different ways the particles of both matter and force interact.
The first term with two Fs is known as the kinetic term. It encapsulates all three forces of nature excluding gravity. It tells us how the bosons, particles that carry energy and forces, will behave and how they will interact with each other.
The second term represents the matter, fermions: electrons, neutrinos, protons etc. This second term describes the energy of the fermionic fields as they change, and also tells us how matter and forces interact.
The third term, h.c., stands for Hermitian conjugate, which is the process cancelling out the problematic particles and infinities that make no sense in this Lagrangian.
The particles described by the Lagrangian thus far are massless. To add mass we need the Higgs field, and that’s what the rest of the Lagrangian deals with. The fourth term describes how the fermionic field interacts with the Higgs field, and tells us how fermions gain the mass from the Higgs field. And, we have another “h.c.” term, but this time Hermitian conjugate tells us how antimatter picks up mass from the Higgs field.
The sixth term tells us
1. how the Higgs field changes in space and time, and
2. how it interacts with the massive bosons of the weak force.
Finally, the last term refers to the potential of the Higgs field. This is like the kinetic terms for the other bosons, but now just for the Higgs. Really, though this term describes the Higgs boson itself.
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