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Spontaneous symmetry breaking is when a system that is symmetric under some symmetry group goes to a vacuum state that is not symmetric, giving rise to phenomena such as the Higgs mechanism.

In QFT, the Lagrangian is a function that summarizes the dynamical properties of the field system and from which the equations of motion can be obtained using the principle of least action.

Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior and interaction of subatomic particles, used in the perturbative approach to QFT.

The path integral formulation of quantum mechanics is a description in which the probabilities of outcomes are calculated by summing over all possible histories of a system.

The electroweak theory unifies the electromagnetic force and the weak nuclear force into a single theory, which is a central part of the Standard Model of particle physics.

QCD is the theory of the strong interaction, describing the interactions of quarks and gluons, and explaining how the strong nuclear force binds protons and neutrons together in atomic nuclei.

Operator field theory is the approach in QFT where fields are treated as operators acting on quantum states of the system, satisfying commutation or anticommutation relations depending on their statistics.

Renormalization is the process in QFT used to tackle infinities that arise in calculated quantities, by systematically adjusting definitions of quantities to keep results finite and predictive.

A quantum field is a field that quantizes the classical fields, providing a quantum description for the fundamental forces of nature, except gravity.

QED is the relativistic quantum field theory of electrodynamics, describing how light and matter interact and providing a framework for explaining the quantum properties of the electromagnetic field.

Gauge invariance is the property of a field theory where the equations of motion do not change under local transformations of the gauge group, which leads to the requirement of gauge bosons to mediate forces.