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An effective field theory describes phenomena below a chosen energy scale by retaining the relevant light fields and organizing local interactions by increasing suppression at that scale.

Spontaneous symmetry breaking occurs when the action and equations have a symmetry but a chosen ground state is invariant only under a proper subgroup. Acting with the broken symmetry generates a degenerate vacuum manifold.

The Standard Model is a gauge theory with gauge group $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_Y$. Its Higgs field breaks the electroweak subgroup to the electromagnetic $U(1{)}_Q$.

Quantum field theory in curved spacetime quantizes matter fields on a prescribed classical spacetime geometry.

The in-in formalism computes expectation values at a finite time by evolving a state forward and backward along a closed time contour. At first order in the interaction Hamiltonian,An $iϵ$ tilt of the early-time contour projects onto the interacting vacuum.

A gauge-theory soliton is a finite-energy localized classical field configuration stabilized by topology or a balance among differently scaling energy terms.

Finite-temperature quantum field theory represents thermal expectation values by evolution through an imaginary-time interval of length $\beta =1/T$.

The large-N expansion organizes an $O(N)$-symmetric theory in powers of $1/N$. At leading order, an auxiliary constraint field is determined by a self-consistent saddle-point or gap equation.

A path integral represents a quantum amplitude or correlation function as an integral over field histories weighted by the exponential of the action.