Symmetries make physics easier to calculate, yet in weak interactions and superconductivity they can break spontaneously. Nambu adapted BCS theory’s mathematics to particle physics and showed that the vacuum lowers its energy by picking one direction in field space. This choice produces massless Goldstone bosons and later led to the Higgs mechanism. Spontaneous symmetry breaking is now central to the Standard Model’s mass generation and to lattice-QCD computations. The concept also influences accelerator design and technologies such as superconducting magnets used in medicine.

Using operator methods and vacuum renormalization, Nambu showed that spontaneous breaking of a global symmetry leads to non-vanishing divergence of the conserved current. The NJL model demonstrated dynamical mass generation, while the Saito-Nambu relation made the Goldstone theorem explicit. Nambu’s framework is indispensable in gauge theories such as electroweak unification and color superconductivity. In effective-field-theory language, a non-zero vacuum expectation value ⟨0|φ|0⟩ acts as an order parameter, reducing a symmetry group G to a subgroup H and producing Nambu–Goldstone modes that dominate low-energy dynamics. These techniques underpin chiral perturbation theory, RG analyses of critical phenomena, and cosmic phase-transition scenarios.

Nambu analyzed a BCS-type Lagrangian, L=ψ̄(i∂̸−m)ψ+G[(ψ̄ψ)^2+(ψ̄iγ_5τψ)^2], and via 1/N expansion derived a dynamical mass gap Σ satisfying the self-consistent condition Σ=−2Gi∫d^4p Tr S_F(p). The symmetry SU(2)_L×SU(2)_R→SU(2)_V yields three NG bosons, foreshadowing modern chiral EFT. From the broken Ward–Takahashi identity he obtained the relation between f_π and the quark condensate ⟨q̄q⟩, consistent with π-decay data. The gauge-extended NJL model anticipated the Higgs mechanism and still guides strong-coupling SUSY dualities, lattice-QCD analyses, and dynamical EWSB scenarios.