The rules can treat every direction equally
A round table has no preferred direction, but a pencil lying on it points somewhere. The table’s symmetry and the pencil’s chosen state are different statements. In physics, the distinction becomes especially powerful when a system’s lowest-energy state chooses among several equivalent possibilities. The equations can retain a symmetry even though the actual ground state does not display it. This is spontaneous symmetry breaking.
The word spontaneous describes how the preference arises from the system’s state. Small disturbances can select one option, and the selected state can persist when the selecting disturbance is removed. A ferromagnet offers a more physical example: below its ordering temperature, many atomic moments can align along one of the allowed directions. The macroscopic direction belongs to the ordered state, while the underlying interactions organize the possible choices.
A finite collection can fluctuate between its possible orientations. The sharp distinction is clearest for a very large system, where changing the orientation of the entire ordered state becomes a collective task. Particle field theory uses the corresponding large-volume vacuum description. Keeping the state and the law separate makes it possible to discuss what is selected, what fluctuates and what symmetry the excitations reveal.
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Superconductivity suggested a new way to think about the vacuum
Yoichiro Nambu saw a deep connection with the new microscopic theory of superconductivity. In a superconductor, the collective electronic state has properties that individual electrons in the normal metal do not display. Excitations can require a finite energy gap. The system’s organization changes what its elementary disturbances look like.
Nambu and Giovanni Jona-Lasinio carried this style of reasoning into particle theory in their 1961 work. They began with interacting fermion fields, the kind of fields used for matter particles, and studied whether the lowest-energy state could organize itself so that the excitations behaved as massive particles. Mass could then arise dynamically from the interacting state, tied to its symmetry properties.
Vacuum in this setting means the lowest-energy state of the fields. It is the reference state around which particles are described as excitations. Treating the vacuum as something with structure opened a new question: which symmetries belong to the equations, and which are visible in the particular vacuum realized by the theory?
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Moving around the low-energy choices creates a light mode
A useful picture is a surface whose lowest points form a circular trough. Moving radially away from the trough costs energy. Moving around the trough changes the chosen direction while staying close to the same energy. In a field theory with a spontaneously broken continuous global symmetry, that soft change appears as a collective mode. In the exact symmetry limit it is massless.
The Nambu–Jona-Lasinio model linked a dynamically generated fermion mass to a pseudoscalar collective state, an idealized pion. Pseudoscalar names how that excitation transforms under spatial reflection. The crucial physical contrast is between a massive matter excitation and a much lighter collective motion of the ordered state. Real pions have a small nonzero mass because the relevant symmetry in nature is approximate.
This relation helped explain why pions are unusually light compared with many other hadrons. The model itself was a simplified effective description, not the final microscopic theory of quarks and gluons. Its lasting contribution was the mechanism and the relation among symmetry, the vacuum and the excitation spectrum.
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The idea spread, with different versions for different fields
Spontaneous symmetry breaking became a common language across condensed matter and particle physics. For a global symmetry, the soft collective mode follows the familiar Nambu–Goldstone reasoning. When the symmetry is gauged, the relation changes: the would-be soft modes can supply the extra polarization states of massive gauge bosons. That is part of the later Brout–Englert–Higgs development.
Nambu received half of the 2008 Nobel Prize for the mechanism of spontaneous broken symmetry in subatomic physics. Kobayashi and Maskawa shared the other half for a different symmetry problem involving quark generations and CP violation. Keeping the two contributions separate makes the common theme clearer: a statement about symmetric laws becomes physically useful only when we ask how the actual states and interactions realize it.